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

Selected Solutions of Einsteins Field Equations: Their Role in General Relativity and Astrophysics

Negative matter is a hypothetical form of matter whose active-gravitational, passive-gravitational, inertial, and rest masses are opposite in sign to normal, positive matter. Negative matter is not antimatter, which as far as is known has normal (positive) mass. If an object made of negative matter could be obtained and coupled by elastic, gravitational, or electromagnetic forces to an object containing an equal amount of positive matter, the interactions between the two objects would result in an unlimited amount of unidirectiona l acceleration of the combination without the requirement for an energy source or reaction mass. In this paper, it is shown in exhaustive detail that, despite their unbelievable propulsive capabilities, negative matter propulsion systems do not violate the Newtonian laws of conservation of linear momentum and energy. Thus, logical objections to the existence of negative matter must be found elsewhere than in Newtonian mechanics. Suggestions are made where evidence for the existence of negative matter might be found.

Negative matter propulsion

Exact Impulsive Gravitational Waves in Spacetimes of Constant Curvature

Asymptotically flat space–times with one Killing vector field are studied. The Killing equations are solved asymptotically using polyhomogeneous expansions (i.e., series in powers of 1/r and ln r), and solved order by order. The solution to the leading terms of these expansions yields the asymptotic form of the Killing vector field. The possible classes of Killing fields are discussed by analyzing their orbits on null infinity. The integrability conditions of the Killing equations are used to obtain constraints on the components of the Weyl tensor (Ψ0,Ψ1,Ψ2) and on the shear (σ). The behavior of the solutions to the constraint equations is studied. It is shown that for Killing fields that are non-supertranslational the characteristics of the constraint equations are the orbits of the restriction of the Killing field to null infinity. As an application, the particular case of boost-rotation symmetric space–times is considered. The constraints on Ψ0 are used to study the behavior of the coefficients that gi...

On Killing vector fields and Newman–Penrose constants

We analyze the directional properties of general gravitational, electromagnetic, and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of I. The standard peeling-off property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for Lambda>0) or timelike (for Lambda 0 the radiation vanishes only along directions which are opposite to principal null directions. For Lambda<0 the directional dependence is more complicated because it is necessary to distinguish outgoing and ingoing radiation. Near such anti-de Sitter-like conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to I. The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This offers a better understanding of the asymptotic behaviour of the fields near conformal infinity.

Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant

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N. S. Swaminarayan

Papers

An exact solution for uniformly accelerated particles in general relativity. III. Singular expanding (contracting) null surface