Author

# F. R. S. Subrahmanyan Chandrasekhar

Bio: F. R. S. Subrahmanyan Chandrasekhar is an academic researcher from University of Chicago. The author has contributed to research in topics: Singularity & Gravitational singularity. The author has an hindex of 6, co-authored 6 publications receiving 112 citations.

##### Papers

More filters

••

TL;DR: In this paper, an exact solution of the Einstein-Maxwell equations is obtained that represents a space-time which describes consistently the collision between two plane impulsive gravitational waves, each supporting an electromagnetic shock-wave.

Abstract: An exact solution of the Einstein—Maxwell equations is obtained that represents a space-time which describes consistently the collision between two plane impulsive gravitational waves, each supporting an electromagnetic shock-wave. In obtaining the solution, the relationship, which had been established earlier, between the solutions describing stationary black-holes and solutions describing colliding plane-waves, is extended to the Einstein-Maxwell equations (and exploited). The case when the colliding waves are parallelly polarized is analysed in detail to exhibit the singularities and the discontinuities that occur on the null boundaries characteristic of this problem. It is found that the passage of the waves, prior to collision, produces a spray of gravitational and electromagnetic radiation and the collision results in the scattering and the focusing of the waves and the development of a space—time singularity. The solution that is obtained avoids in a natural way certain conceptual difficulties (such as the occurrence of the ‘square root’ of a δ -function and current sheets) that had been anticipated.

41 citations

••

TL;DR: In this paper, a colliding plane gravitational wave that leads to the development of a horizon and a subsequent time-like singularity is coupled with an electromagnetic field, a perfect fluid (whose energy density, ε, equals the pressure, p), and null dust (consisting of massless particles).

Abstract: Colliding plane gravitational waves that lead to the development of a horizon and a subsequent time-like singularity are coupled with an electromagnetic field, a perfect fluid (whose energy density, $\epsilon$, equals the pressure, p), and null dust (consisting of massless particles) The coupling of the gravitational waves with an electromagnetic field does not affect, in any essential way, the development of the horizon or the time-like singularity if the polarizations of the colliding gravitational waves are not parallel If the polarizations are parallel, the space-like singularity which occurs in the vacuum is transformed into a horizon followed by a three-dimensional time-like singularity by the merest presence of the electromagnetic field The coupling of the gravitational waves with an ($\epsilon$ = p)-fluid and null dust affect the development of horizons and singularities in radically different ways: the ($\epsilon$ = p)-fluid affects the development decisively in all cases but qualitatively in the same way, while null dust prevents the development of horizons and allows only the development of space-like singularities The contrasting behaviours of an ($\epsilon$ = p)-fluid and of null dust in the framework of general relativity is compared with the behaviours one may expect, under similar circumstances, in the framework of special relativity

22 citations

••

TL;DR: In this paper, the axisymmetric perturbations of static space-times with prevailing sources (a Maxwell field or a perfect fluid) are considered; and it is shown how a flux integral can be derived directly from the relevant linearized equations.

Abstract: The axisymmetric perturbations of static space-times with prevailing sources (a Maxwell field or a perfect fluid) are considered; and it is shown how a flux integral can be derived directly from the relevant linearized equations. The flux integral ensures the conservation of energy in the attendant scattering of radiation and the sometimes accompanying transformation of one kind of radiation into another. The flux integral derived for perturbed Einstein-Maxwell space-times will be particularly useful in this latter context (as in the scattering of radiation by two extreme Reissner-Nordstrom black-holes) and in the setting up of a scattering matrix. And the flux integral derived for a space-time with a perfect-fluid source will be directly applicable to the problem of the non-radial oscillations of a star with accompanying emission of gravitational radiation and enable its reformulation as a problem in scattering theory.

22 citations

••

TL;DR: In this paper, an axisymmetric solution of the Einstein-Maxwell equations is found which represents the static placement of two charged black holes of equal mass (M) and opposite charge (? Q) with IQI > M. The solution obtained in this paper is analogous to the equilibrium solution one has found, at the quantal level, for Dirac magnetic monopoles connected by strings.

Abstract: An axisymmetric solution of the Einstein-Maxwell equations is found which represents the static placement of two charged black holes of equal mass (M) and opposite charge (? Q) with IQI > M. The space-time, external to the event horizons of the two black holes, is asymptotically flat and entirely smooth except for the occurrence, on the axis, of a simple conical singularity with deficit. In other words, a ' string' stretches along the axis of symmetry and provides support for the black holes. In the extended space-time, interior to the horizons of the black holes, time-like curvature singularities, with two spatial dimensions, do occur. And, finally, the surface gravity that prevails on the horizons of the two black holes vanishes. This transgression of the two theorems, excluding the existence of multiple black holes except those of the extreme Reissner-Nordstrom type and requiring IQI AM for isolated black holes, is made possible by relaxing the strict requirements of smoothness to the extent of allowing conical singularities. The solution obtained in this paper is, at the classical level, analogous to the equilibrium solution one has found, at the quantal level, for Dirac magnetic monopoles connected by strings. In this paper, we shall obtain a static axisymmetric solution of the EinsteinMaxwell equations that follows from the simplest solution of the X- and Yequations (see ? 3(b) of the preceding paper, Chandrasekhar (I989 b), referred to hereafter as Paper I; familiarity with the notations and definitions of this paper will be assumed). The solution represents the static placement, on the axis of symmetry, of two charged black holes of equal mass (M) and opposite charge (? Q) with IQI > M. Besides, the two black holes are attached to 'strings'. A string for the purposes of this paper is a line in space-time along which a conical singularity (with no associated curvature singularity) occurs characterized by a deficit defined by the difference between 2ir and the limiting ratio of the circumference to the proper radius of a small circle described normal to the line. For the solution that is obtained the string (in general) stretches along the entire axis with the deficit along the part of the axis joining the black holes being less than that along this axis extending to + oo and - oo from the north pole of the one and the south pole of the other. Except for the occurrence of the simple conical singularity along the

14 citations

••

TL;DR: In this paper, an exact solution to describe the dispersion of a wave packet of gravita-tional radiation, having initially (at time t = 0) an impulsive character, was analyzed.

Abstract: An exact solution, describing the dispersion of a wave packet of gravitational radiation, having initially (at time t = 0) an impulsive character, is analysed. The impulsive character of the wave-packet derives from the space-time being flat, except at a radial distance ϖ = ϖ 1 (say) at t = 0, and the time-derivative of the Weyl scalars exhibiting δ-function singularities at ϖ = ϖ 1 , when t → 0. The principal feature of the dispersion is the development of a singularity of the metric function, v , and of the Weyl scalar, ψ 2 , when the wave, after reflection at the centre, collides with the still incoming waves. The evolution of the metric functions and of the Weyl scalars, as the dispersion progresses, is illustrated graphically.

9 citations

##### Cited by

More filters

••

208 citations

••

TL;DR: In this paper, the authors show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter.

Abstract: Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with aC0 metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational “shock waves” at the horizon of a Schwarzschild black hole, and (2) a configuration involving onlyone external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the “Wheeler wormhole” to another universe.

149 citations

•

TL;DR: In this article, the authors introduce the Schwarzschild-Kruskal spacetime and the Reissner-Nordstrom solution, and discuss the role of explicit solutions in other parts of physics and astrophysics.

Abstract: Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de Sitter spacetimes. On the interpretation and characterization of metrics. The choice of solutions. The outline] 2) The Schwarzschild solution [Spherically symmetric spacetimes. The Schwarzschild metric and its role in the solar system. Schwarzschild metric outside a collapsing star. The Schwarzschild-Kruskal spacetime. The Schwarzschild metric as a case against Lorentz-covariant approaches. The Schwarzschild metric and astrophysics] 3) The Reissner- Nordstrom solution [Reissner-Nordstrom black holes and the question of cosmic censorship. On extreme black holes, d-dimensional black holes, string theory and "all that"] 4) The Kerr metric [Basic features. The physics and astrophysics around rotating black holes. Astrophysical evidence for a Kerr metric] 5) Black hole uniqueness and multi-black hole solutions 6) Stationary axisymmetric fields and relativistic disks [Static Weyl metrics. Relativistic disks as sources of the Kerr metric and other stationary spacetimes. Uniformly rotating disks] 7) Taub-NUT space [A new way to the NUT metric. Taub-NUT pathologies and applications] 8) Plane waves and their collisions [Plane-fronted waves. New developments and applications. Colliding plane waves] 9) Cylindrical waves [Cylindrical waves and the asymptotic structure of 3-dimensional general relativity. Cylindrical waves and quantum gravity. Cylindrical waves: a miscellany] 10) On the Robinson-Trautman solutions 11) The boost-rotation symmetric radiative spacetimes 12) The cosmological models [Spatially homogeneous cosmologies. Inhomogeneous models] 13) Concluding remarks

124 citations

•

TL;DR: In this article, the formation, physical properties and cosmological evolution of various topological defects such as vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings are reviewed.

Abstract: Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.

98 citations

••

TL;DR: In this article, the authors constructed exact solutions to Einstein's equation containing two colliding planar shells of matter which divide spacetime into four regions, three of which are flat.

Abstract: Using methods similar to those in a previous paper, (Dray and 't Hooft 1985), the authors construct exact solutions to Einstein's equation containing two colliding planar shells of matter which divide spacetime into four regions, three of which are flat. In the appendices they consider some more general cases.

70 citations