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109-430: Since 1953, The Astrophysical Journal Supplement Series ( ApJS ) has been published in conjunction with The Astrophysical Journal , with generally longer articles to supplement the material in the journal. It publishes six volumes per year, with two 280-page issues per volume. The Astrophysical Journal Letters ( ApJL ), established in 1967 by Subrahmanyan Chandrasekhar as Part 2 of The Astrophysical Journal ,

218-540: A Google Doodle in 28 countries honouring Chandrasekhar's 107th birthday and the Chandrasekhar limit . In 2010, on account of Chandra's 100th birthday, University of Chicago conducted a symposium titled Chandrasekhar Centennial Symposium 2010 which was attended by leading astrophysicists such as Roger Penrose , Kip Thorne , Freeman Dyson , Jayant V. Narlikar , Rashid Sunyaev , G. Srinivasan , and Clifford Will . Its research talks were published in 2011 as

327-555: A Tamil family, to Sita Balakrishnan (1891–1931) and Chandrasekhara Subrahmanya Ayyar (1885–1960) who was stationed in Lahore as Deputy Auditor General of the Northwestern Railways at the time of Chandrasekhar's birth. He had two elder sisters, Rajalakshmi and Balaparvathi, three younger brothers, Vishwanathan, Balakrishnan, and Ramanathan, and four younger sisters, Sarada, Vidya, Savitri, and Sundari. His paternal uncle

436-621: A heart attack at the University of Chicago Hospital in 1995, having survived a prior heart attack in 1975. He was survived by his wife, who died on 2 September 2013 at the age of 102. She was a serious student of literature and western classical music. Once when involved in a discussion about the Bhagavad Gita , Chandrasekhar said: "I should like to preface my remarks with a personal statement in order that my later remarks will not be misunderstood. I consider myself an atheist". This

545-469: A November 1783 letter to Henry Cavendish , and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke , who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta , notorious as a prison where people entered but never left alive. The term "black hole"

654-428: A Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a limit. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by

763-507: A black hole acts like an ideal black body , as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation , with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes , making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for light to escape were first considered in

872-506: A black hole appears to slow as it approaches the event horizon, taking an infinite amount of time to reach it. At the same time, all processes on this object slow down, from the viewpoint of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift . Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than

981-462: A black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Any matter that falls toward a black hole can form an external accretion disk heated by friction , forming quasars , some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shredded into streamers that shine very brightly before being "swallowed." If other stars are orbiting

1090-489: A black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine whether such an event occurred. As predicted by general relativity,

1199-512: A black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M , through where r s is the Schwarzschild radius and M ☉ is the mass of the Sun . For a black hole with nonzero spin and/or electric charge, the radius is smaller, until an extremal black hole could have an event horizon close to The defining feature of

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1308-524: A black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems and established that the radio source known as Sagittarius A* , at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses. The idea of

1417-455: A body so big that even light could not escape was briefly proposed by English astronomical pioneer and clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that one would form when a star's diameter exceeds the Sun's by a factor of 500, and its surface escape velocity exceeds

1526-541: A book titled Fluid flows to Black Holes: A tribute to S Chandrasekhar on his birth centenary . Chandrasekhar published around 380 papers in his lifetime. He wrote his first paper in 1928 when he was still an undergraduate student about Compton effect and last paper which was accepted for publication just two months before his death was in 1995 which was about non-radial oscillation of stars. The University of Chicago Press published selected papers of Chandrasekhar in seven volumes. Black hole A black hole

1635-454: A bronze medal for his work on degenerate stars, in the summer of 1933, Chandrasekhar was awarded his PhD degree at Cambridge with a thesis among his four papers on rotating self-gravitating polytropes . On 9 October, he was elected to a Prize Fellowship at Trinity College for the period 1933–1937, becoming only the second Indian to receive a Trinity Fellowship after Srinivasa Ramanujan 16 years earlier. He had been so certain of failing to obtain

1744-462: A central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), for which any infinitesimal inward perturbations to a circular orbit will lead to spiraling into the black hole, and any outward perturbations will, depending on the energy, result in spiraling in, stably orbiting between apastron and periastron, or escaping to infinity. The location of

1853-560: A course at the University of Chicago. Two of the students who took the course, Tsung-Dao Lee and Chen-Ning Yang , won the Nobel prize before he could get one for himself. Regarding classroom interactions during his lectures, noted astrophysicist Carl Sagan stated from firsthand experience that "frivolous questions" from unprepared students were "dealt with in the manner of a summary execution", while questions of merit "were given serious attention and response". From 1952 to 1971 Chandrasekhar

1962-443: A course organised by Struve, was vetoed by the dean Henry Gale based on a racial prejudice; Hutchins said "By all means have Mr.Chandrasekhar teach". Chandrasekhar remained at the University of Chicago for his entire career. He was promoted to associate professor in 1941 and to full professor two years later at the age of 33. In 1946, when Princeton University offered Chandrasekhar a position vacated by Henry Norris Russell with

2071-404: A density as the Sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the spacetime metric that space would close up around

2180-401: A fellow student at Presidency College . He became a naturalised citizen of the U.S. in 1953. Many considered him as warm, positive, generous, unassuming, meticulous, and open to debate, while some others as private, intimidating, impatient and stubborn regarding non-scientific matters, and unforgiving to those who ridiculed his work. Chandrasekhar was a vegetarian . Chandrasekhar died of

2289-538: A lecture by Arnold Sommerfeld . He obtained his bachelor's degree, BSc (Hon.), in physics, in June 1930. In July 1930, Chandrasekhar was awarded a Government of India scholarship to pursue graduate studies at the University of Cambridge , where he was admitted to Trinity College , secured by R. H. Fowler with whom he communicated his first paper. During his travels to England , Chandrasekhar spent his time working out

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2398-473: A mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. The first black hole known was Cygnus X-1 , identified by several researchers independently in 1971. Black holes of stellar mass form when massive stars collapse at

2507-403: A naming contest which attracted 6,000 entries from fifty states and sixty-one countries. The Chandra X-ray Observatory was launched and deployed by Space Shuttle Columbia on 23 July 1999. The Chandrasekhar number , an important dimensionless number of magnetohydrodynamics , is named after him. The asteroid 1958 Chandra is also named after Chandrasekhar. The Himalayan Chandra Telescope

2616-418: A new quantity he termed " dynamical friction ", which has the dual effects of decelerating the star and helping to stabilize clusters of stars. Chandrasekhar extended this analysis to the interstellar medium, showing that clouds of galactic gas and dust are distributed very unevenly. Chandrasekhar studied at Presidency College, Madras (now Chennai ) and the University of Cambridge . A long-time professor at

2725-431: A non-rotating black hole, this region takes the shape of a single point; for a rotating black hole it is smeared out to form a ring singularity that lies in the plane of rotation. In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density . Observers falling into

2834-565: A salary double that of Chicago's, Hutchins incremented his salary matching with that of Princeton's and persuaded Chandrasekhar to stay in Chicago. In 1952, he became Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics and Enrico Fermi Institute , upon Enrico Fermi 's invitation. In 1953, he and his wife, Lalitha Chandrasekhar, took American citizenship. After the Laboratory for Astrophysics and Space Research (LASR)

2943-495: A second. On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle . The topology of

3052-419: A situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity . It is generally expected that such a theory will not feature any singularities. The photon sphere

3161-554: A student of Hendrik Lorentz , independently gave the same solution for the point mass and wrote more extensively about its properties. This solution had a peculiar behaviour at what is now called the Schwarzschild radius , where it became singular , meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that

3270-411: A unique style of mastering several fields of physics and astrophysics; consequently, his working life can be divided into distinct periods. He would exhaustively study a specific area, publish several papers in it and then write a book summarizing the major concepts in the field. He would then move on to another field for the next decade and repeat the pattern. Thus he studied stellar structure , including

3379-417: A wave rather than a particle, it was unclear what, if any, influence gravity would have on escaping light waves. The modern theory of gravity, general relativity, discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface. Instead, spacetime itself is curved such that

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3488-508: Is a region of spacetime wherein gravity is so strong that no matter or electromagnetic energy (e.g. light ) can escape it. Albert Einstein 's theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon . A black hole has a great effect on the fate and circumstances of an object crossing it, but it has no locally detectable features according to general relativity. In many ways,

3597-432: Is a spherical boundary where photons that move on tangents to that sphere would be trapped in a non-stable but circular orbit around the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable , hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting

3706-594: Is identical to that of any other body of the same mass. Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric , while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum. While

3815-534: Is named after him. In the Biographical Memoirs of Fellows of the Royal Society of London , R. J. Tayler wrote: "Chandrasekhar was a classical applied mathematician whose research was primarily applied in astronomy and whose like will probably never be seen again." Chandrasekhar supervised 45 PhD students. After his death, his wife Lalitha Chandrasekhar made a gift of his Nobel Prize money to

3924-547: Is now a separate journal focusing on the rapid publication of high-impact astronomical research. The three journals were published by the University of Chicago Press for the American Astronomical Society until, in January 2009, publication was transferred to IOP Publishing , following the move of the society's Astronomical Journal in 2008. The reason for the changes were given by the society as

4033-548: Is taken from the rotational energy of the black hole. Thereby the rotation of the black hole slows down. A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei . In Newtonian gravity , test particles can stably orbit at arbitrary distances from

4142-409: Is the only vacuum solution that is spherically symmetric . This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore correct only near a black hole's horizon; far away, the external gravitational field

4251-414: Is the result of a process known as frame-dragging ; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the speed of light in

4360-552: Is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17  M ☉ . Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. The hypothetical collapsed stars were called "frozen stars", because an outside observer would see

4469-928: The Aberdeen Proving Ground in Maryland. While there, he worked on problems of ballistics , resulting in reports such as 1943's On the decay of plane shock waves , Optimum height for the bursting of a 105mm shell , On the Conditions for the Existence of Three Shock Waves , On the Determination of the Velocity of a Projectile from the Beat Waves Produced by Interference with the Waves of Modified Frequency Reflected from

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4578-520: The Chandrasekhar limit and the Chandra X-Ray Observatory , are named after him. Chandrasekhar worked on a wide variety of problems in physics during his lifetime, contributing to the contemporary understanding of stellar structure , white dwarfs , stellar dynamics , stochastic process , radiative transfer , the quantum theory of the hydrogen anion , hydrodynamic and hydromagnetic stability, turbulence , equilibrium and

4687-763: The Creative Commons license CC-BY-SA 4.0. Non-open access articles accepted before that date will be free to access but will still need permission to reuse. The journal was founded in 1895 by George Ellery Hale and James E. Keeler as The Astrophysical Journal: An International Review of Spectroscopy and Astronomical Physics . In addition to the two founding editors, there was an international board of associate editors: M. A. Cornu , Paris; N. C. Dunér , Upsala; William Huggins , London; P. Tacchini , Rome; H. C. Vogel , Potsdam, C. S. Hastings , Yale; A. A. Michelson , Chicago; E. C. Pickering , Harvard; H. A. Rowland , Johns Hopkins; and C. A. Young , Princeton. It

4796-700: The LIGO Scientific Collaboration and the Virgo collaboration announced the first direct detection of gravitational waves , representing the first observation of a black hole merger. On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope (EHT) in 2017 of the supermassive black hole in Messier 87's galactic centre . As of 2023 ,

4905-540: The Nobel Prize in Physics in 1983 for his studies on the physical processes important to the structure and evolution of stars . Chandrasekhar accepted this honour, but was upset the citation mentioned only his earliest work, seeing it as a denigration of a lifetime's achievement. He shared it with William A. Fowler . Chandrasekhar's most notable work is on the astrophysical Chandrasekhar limit . The limit gives

5014-483: The Oppenheimer–Snyder model in their paper "On Continued Gravitational Contraction", which predicted the existence of black holes. In the paper, which made no reference to Einstein's recent publication, Oppenheimer and Snyder used Einstein's own theory of general relativity to show the conditions on how a black hole could develop, for the first time in contemporary physics. In 1958, David Finkelstein identified

5123-637: The University of Chicago towards the establishment of the Subrahmanyan Chandrasekhar Memorial Fellowship. First awarded in the year 2000, this fellowship is given annually to an outstanding applicant to graduate school in the PhD programs of the department of physics or the department of astronomy and astrophysics. S. Chandrasekhar Prize of Plasma Physics is an award given by Association of Asia Pacific Physical Societies (AAPS) to outstanding plasma physicists, started in

5232-668: The University of Chicago , he did some of his studies at the Yerkes Observatory , and served as editor of The Astrophysical Journal from 1952 to 1971. He was on the faculty at Chicago from 1937 until his death in 1995 at the age of 84, and was the Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics. Subrahmanyan was born in Lahore on 19 October 1910 of the British Raj (present-day Pakistan ) in

5341-519: The geodesic that light travels on never leaves the surface of the "star" (black hole). In 1915, Albert Einstein developed his theory of general relativity , having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations that describes the gravitational field of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste ,

5450-409: The statistical mechanics of the degenerate electron gas in white dwarf stars, providing relativistic corrections to Fowler's previous work (see Legacy below). In his first year at Cambridge, as a research student of Fowler, Chandrasekhar spent his time calculating mean opacities and applying his results to the construction of an improved model for the limiting mass of the degenerate star. At

5559-431: The 18th century by John Michell and Pierre-Simon Laplace . In 1916, Karl Schwarzschild found the first modern solution of general relativity that would characterise a black hole. Due to his influential research, the Schwarzschild metric is named after him. David Finkelstein , in 1958, first published the interpretation of "black hole" as a region of space from which nothing can escape. Black holes were long considered

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5668-435: The 1960s, he studied both the equilibrium and the stability of ellipsoidal figures of equilibrium, and general relativity. During the period, 1971 to 1983 he studied the mathematical theory of black holes , and, finally, during the late 80s, he worked on the theory of colliding gravitational waves . Chandra worked closely with his students and expressed pride in the fact that over a 50-year period (from roughly 1930 to 1980),

5777-490: The 2020 Nobel Prize in Physics , Hawking having died in 2018. Based on observations in Greenwich and Toronto in the early 1970s, Cygnus X-1 , a galactic X-ray source discovered in 1964, became the first astronomical object commonly accepted to be a black hole. Work by James Bardeen , Jacob Bekenstein , Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics . These laws describe

5886-401: The Kerr singularity, which leads to problems with causality like the grandfather paradox . It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes. The appearance of singularities in general relativity is commonly perceived as signalling the breakdown of the theory. This breakdown, however, is expected; it occurs in

5995-580: The Projectile and The normal reflection of a blast wave . Chandrasekhar's expertise in hydrodynamics led Robert Oppenheimer to invite him to join the Manhattan Project at Los Alamos, but delays in the processing of his security clearance prevented him from contributing to the project. It has been rumoured that he visited the Calutron project. He wrote that his scientific research

6104-505: The Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction". This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal , who

6213-568: The age of 12. In middle school his father taught him mathematics and physics and his mother taught him Tamil . He later attended the Hindu High School , Triplicane , Madras during the years 1922–25. Subsequently, he studied at Presidency College, Madras (affiliated to the University of Madras ) from 1925 to 1930, writing his first paper, "The Compton Scattering and the New Statistics ", in 1929 after being inspired by

6322-483: The average age of his co-author collaborators had remained the same, at around 30. He insisted that students address him as "Prof. Chandrasekhar" until they received their PhD degree, after which time they (as other colleagues) were encouraged to address him as "Chandra". When Chandrasekhar was working at the Yerkes Observatory in 1940s, he would drive 150 miles (240 km) to and from every weekend to teach

6431-463: The behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy , and surface gravity to temperature . The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation . On 11 February 2016,

6540-498: The black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number . This behaviour is so puzzling that it has been called the black hole information loss paradox . The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916. According to Birkhoff's theorem , it

6649-537: The collapse. They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star , which is itself stable. In 1939, Robert Oppenheimer and others predicted that neutron stars above another limit, the Tolman–Oppenheimer–Volkoff limit , would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics

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6758-448: The discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole . Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged . Through

6867-407: The end of their life cycle. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of solar masses ( M ☉ ) may form by absorbing other stars and merging with other black holes, or via direct collapse of gas clouds . There is consensus that supermassive black holes exist in the centres of most galaxies . The presence of

6976-400: The event horizon of a black hole at equilibrium is always spherical. For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate. At the centre of a black hole, as described by general relativity, may lie a gravitational singularity , a region where the spacetime curvature becomes infinite. For

7085-458: The fellowship that he had already made arrangements to study under Milne that autumn at Oxford, even going to the extent of renting a flat there. During this time, Chandrasekhar became acquainted with British physicist Sir Arthur Eddington . Eddington took an interest in his work, but in January, 1935, gave a talk severely criticizing Chandrasekhar's work (see #Dispute with Eddington and Chandrasekhar–Eddington dispute ). In 1935, Chandrasekhar

7194-648: The growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect". In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole . The possibility of travelling to another universe is, however, only theoretical since any perturbation would destroy this possibility. It also appears to be possible to follow closed timelike curves (returning to one's own past) around

7303-580: The increasing financial demands of the University of Chicago Press. Compared to journals in other scientific disciplines, The Astrophysical Journal has a larger (> 85%) acceptance rate, which, however, is similar to other journals covering astronomy and astrophysics. On January 1, 2022, the AAS Journals, including ApJ, changed to an open access model, with access restrictions and subscription charges removed from previously published papers. Articles accepted after October 11, 2022, will be published under

7412-608: The language and methods of ordinary calculus. The effort resulted in the book Newton's Principia for the Common Reader , published in 1995. Chandrasekhar also worked on collision of gravitational waves, and algebraically special perturbations. Chandrasekhar was the nephew of C. V. Raman , who was awarded the Nobel Prize for Physics in 1930. Chandrasekhar married Lalitha Doraiswamy in September 1936. He met her as

7521-544: The mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. The total electric charge  Q and the total angular momentum  J are expected to satisfy the inequality for a black hole of mass M . Black holes with the minimum possible mass satisfying this inequality are called extremal . Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from

7630-437: The mass of a white dwarf could not exceed 1.44 times that of the Sun – the Chandrasekhar limit . Chandrasekhar revised the models of stellar dynamics first outlined by Jan Oort and others by considering the effects of fluctuating gravitational fields within the Milky Way on stars rotating about the galactic centre. His solution to this complex dynamical problem involved a set of twenty partial differential equations, describing

7739-452: The maximum mass of a white dwarf star, ~1.44 solar masses , or equivalently, the minimum mass that must be exceeded for a star to collapse into a neutron star or black hole (following a supernova ). The limit was first calculated by Chandrasekhar in 1930 during his maiden voyage from India to Cambridge, England for his graduate studies. In 1979, NASA named the third of its four " Great Observatories " after Chandrasekhar. This followed

7848-678: The meetings of the Royal Astronomical Society , he met E. A. Milne . At the invitation of Max Born he spent the summer of 1931, his second year of post-graduate studies, at Born's institute at Göttingen , working on opacities, atomic absorption coefficients , and model stellar photospheres . On the advice of P. A. M. Dirac , he spent his final year of graduate studies at the Institute for Theoretical Physics in Copenhagen , where he met Niels Bohr . After receiving

7957-414: The microscopic level, because they are time-reversible . Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from

8066-479: The nearest known body thought to be a black hole, Gaia BH1 , is around 1,560 light-years (480 parsecs ) away. Though only a couple dozen black holes have been found so far in the Milky Way, there are thought to be hundreds of millions, most of which are solitary and do not cause emission of radiation. Therefore, they would only be detectable by gravitational lensing . John Michell used the term "dark star" in

8175-508: The opposite direction to just stand still. The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ergosurface , which coincides with the event horizon at the poles but is at a much greater distance around the equator. Objects and radiation can escape normally from the ergosphere. Through the Penrose process , objects can emerge from the ergosphere with more energy than they entered with. The extra energy

8284-663: The other opening had been filled by Bengt Stromgren , a Danish theorist. Following a recommendation from Kuiper, Struve invited Chandrasekhar to Yerkes in March 1936 and offered him the job. Though Chandrasekhar was keenly interested, he initially declined the offer and left for England; after Hutchins sent a radiogram to Chandrasekhar during the voyage, he finally accepted, returning to Yerkes as an assistant professor of Theoretical Astrophysics in December 1936. Hutchins also intervened on an occasion where Chandra's participation on teaching

8393-425: The outside, and hence are deemed unphysical . The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter . This is supported by numerical simulations. Due to the relatively large strength of the electromagnetic force , black holes forming from the collapse of stars are expected to retain the nearly neutral charge of

8502-418: The photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon. While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between

8611-399: The photon sphere and the event horizon. For a Kerr black hole the radius of the photon sphere depends on the spin parameter and on the details of the photon orbit, which can be prograde (the photon rotates in the same sense of the black hole spin) or retrograde. Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This

8720-458: The presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole. To a distant observer, clocks near a black hole would appear to tick more slowly than those farther away from the black hole. Due to this effect, known as gravitational time dilation , an object falling into

8829-414: The same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics is currently an unsolved problem. These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly,

8938-498: The scientific knowledge about the structure of stars, stellar evolution and black holes. He was awarded the 1983 Nobel Prize in physics along with William A. Fowler for theoretical studies of the physical processes of importance to the structure and evolution of the stars. His mathematical treatment of stellar evolution yielded many of the current theoretical models of the later evolutionary stages of massive stars and black holes . Many concepts, institutions and inventions, including

9047-478: The shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behaviour of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance —the membrane paradigm . This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at

9156-406: The singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky , Isaak Khalatnikov , and Evgeny Lifshitz , who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically. For this work, Penrose received half of

9265-506: The singularity disappeared after a change of coordinates. In 1933, Georges Lemaître realised that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity . Arthur Eddington commented on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high

9374-417: The stability of ellipsoidal figures of equilibrium , general relativity , mathematical theory of black holes and theory of colliding gravitational waves. At the University of Cambridge , he developed a theoretical model explaining the structure of white dwarf stars that took into account the relativistic variation of mass with the velocities of electrons that comprise their degenerate matter. He showed that

9483-452: The star, leaving us outside (i.e., nowhere)." In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4  M ☉ ) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and Lev Landau , who argued that some yet unknown mechanism would stop

9592-436: The star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105 appears to have an angular momentum near the maximum allowed value. That uncharged limit is allowing definition of a dimensionless spin parameter such that Black holes are commonly classified according to their mass, independent of angular momentum, J . The size of

9701-428: The surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius. Also in 1939, Einstein attempted to prove that black holes were impossible in his publication "On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses", using his theory of general relativity to defend his argument. Months later, Oppenheimer and his student Hartland Snyder provided

9810-432: The term for its brevity and "advertising value", and it quickly caught on, leading some to credit Wheeler with coining the phrase. The no-hair theorem postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share

9919-410: The theory of white dwarfs , during the years 1929 to 1939, and subsequently focused on stellar dynamics , theory of Brownian motion from 1939 to 1943. Next, he concentrated on the theory of radiative transfer and the quantum theory of the negative ion of hydrogen from 1943 to 1950. This was followed by sustained work on turbulence and hydrodynamic and hydromagnetic stability from 1950 to 1961. In

10028-521: The total mass inside a sphere containing a black hole can be found by using the gravitational analogue of Gauss's law (through the ADM mass ), far away from the black hole. Likewise, the angular momentum (or spin) can be measured from far away using frame dragging by the gravitomagnetic field , through for example the Lense–Thirring effect . When an object falls into a black hole, any information about

10137-484: The two compared each other's theories in publications. Chandrasekhar ultimately completed his theory of white dwarfs in 1939, receiving praise from others in the field. Eddington died in 1944, and despite their disagreements, Chandrasekhar continued to state that he admired Eddington and considered him a friend. During World War II, Chandrasekhar worked at the Ballistic Research Laboratory at

10246-436: The usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. Scholars of the time were initially excited by the proposal that giant but invisible 'dark stars' might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century, as if light were

10355-484: The work of Werner Israel , Brandon Carter , and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric : mass , angular momentum , and electric charge. At first, it was suspected that the strange features of the black hole solutions were pathological artefacts from the symmetry conditions imposed, and that

10464-479: The year 2014. The Chandra Astrophysics Institute (CAI) is a program offered for high school students who are interested in astrophysics mentored by MIT scientists and sponsored by the Chandra X-ray Observatory . Carl Sagan praised him in the book The Demon-Haunted World : "I discovered what true mathematical elegance is from Subrahmanyan Chandrasekhar." On 19 October 2017, Google showed

10573-469: Was also confirmed many times in his other talks. Kameshwar C. Wali quoted him saying: "I am not religious in any sense; in fact, I consider myself an atheist." In an interview with Kevin Krisciunas at the University of Chicago, on 6 October 1987, Chandrasekhar commented: "Of course, he ( Otto Struve ) knew I was an atheist, and he never brought up the subject with me". Chandrasekhar was awarded half of

10682-410: Was built by NASA in 1966 at the university, Chandrasekhar occupied one of the four corner offices on the second floor. (The other corners housed John A. Simpson , Peter Meyer , and Eugene N. Parker .) Chandrasekhar lived at 4800 Lake Shore Drive after the high-rise apartment complex was built in the late 1960s, and later at 5550 Dorchester Building. After graduating from Cambridge, Chandrasekhar, who

10791-629: Was editor of The Astrophysical Journal . When Eugene Parker submitted a paper on his discovery of solar wind in 1957, two eminent reviewers rejected the paper. However, since Chandra as an editor could not find any mathematical flaws in Parker's work, he went ahead and published the paper in 1958. During the years 1990 to 1995, Chandrasekhar worked on a project devoted to explaining the detailed geometric arguments in Sir Isaac Newton 's Philosophiae Naturalis Principia Mathematica using

10900-684: Was in close contact with Arthur Eddington, presented a full solution to his stellar equation at the Royal Astronomical Society meeting in 1935. Eddington booked a talk right after Chandrasekhar, where he openly criticized Chandrasekhar's theory. This depressed Chandrasekhar and sparked a scientific dispute. Eddington refused to accept a limit for the mass of a star and was proposing an alternative model. Chandrasekhar sought support from prominent physicists like Léon Rosenfeld , Niels Bohr and Christian Møller who found Eddington's arguments lacking. The tension persisted through 1930s, as Eddington continued to openly criticize Chandrasekhar during meetings and

11009-541: Was intended that the journal would fill the gap between journals in astronomy and physics, providing a venue for publication of articles on astronomical applications of the spectroscope ; on laboratory research closely allied to astronomical physics, including wavelength determinations of metallic and gaseous spectra and experiments on radiation and absorption ; on theories of the Sun, Moon, planets, comets, meteors, and nebulae; and on instrumentation for telescopes and laboratories. The further development of ApJ up to 1995

11118-563: Was invited by the director of the Harvard Observatory, Harlow Shapley , to be a visiting lecturer in theoretical astrophysics for a three-month period. He travelled to the United States in December. During his visit to Harvard, Chandrasekhar greatly impressed Shapley, but declined his offer of a Harvard research fellowship. At the same time, Chandrasekhar met Gerard Kuiper , a noted Dutch astrophysical observationalist who

11227-483: Was likely to intervene and stop at least some stars from collapsing to black holes. Their original calculations, based on the Pauli exclusion principle , gave it as 0.7  M ☉ . Subsequent consideration of neutron-neutron repulsion mediated by the strong force raised the estimate to approximately 1.5  M ☉ to 3.0  M ☉ . Observations of the neutron star merger GW170817 , which

11336-496: Was motivated by his desire to participate in the progress of different subjects in science to the best of his ability, and that the prime motive underlying his work was systematization . "What a scientist tries to do essentially is to select a certain domain, a certain aspect, or a certain detail, and see if that takes its appropriate place in a general scheme which has form and coherence; and, if not, to seek further information which would help him to do that". Chandrasekhar developed

11445-515: Was outlined by Helmut Abt in an article entitled "Some Statistical Highlights of the Astrophysical Journal " in 1995. The following persons have been editors-in-chief of the journal: Subrahmanyan Chandrasekhar Subrahmanyan Chandrasekhar FRS ( / ˌ tʃ ə n d r ə ˈ ʃ eɪ k ər / ; 19 October 1910 – 21 August 1995) was an Indian-American theoretical physicist who made significant contributions to

11554-510: Was the Indian physicist and Nobel laureate Chandrasekhara Venkata Raman . His mother was devoted to intellectual pursuits, had translated Henrik Ibsen 's A Doll's House into Tamil and is credited with arousing Chandra's intellectual curiosity at an early age. The family moved from Lahore to Allahabad in 1916, and finally settled in Madras in 1918. Chandrasekhar was tutored at home until

11663-464: Was then a leading authority on white dwarfs. Kuiper had recently been recruited by Otto Struve , the director of the Yerkes Observatory in Williams Bay, Wisconsin , which was run by the University of Chicago , and the university's president, Robert Maynard Hutchins . Having known of Chandrasekhar, Struve was then considering him for one of three faculty posts in astrophysics, along with Kuiper;

11772-461: Was urged to publish it. These results came at the beginning of the golden age of general relativity , which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967, which, by 1969, were shown to be rapidly rotating neutron stars. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but

11881-656: Was used in print by Life and Science News magazines in 1963, and by science journalist Ann Ewing in her article " 'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio. In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler ; Wheeler adopted

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