Selected solutions of Einstein's field equations: their role in general relativity and astrophysics

TL;DR

This paper reviews key exact solutions of Einstein's field equations, discussing their physical interpretations, roles in astrophysics, and recent developments, highlighting their importance in understanding gravitational phenomena and spacetime structures.

Contribution

It provides a comprehensive overview of classical and recent solutions of Einstein's equations, emphasizing their significance in astrophysics and theoretical physics, with insights into new developments and applications.

Findings

Schwarzschild solution's role in solar system dynamics

Reissner-Nordstrom black holes and cosmic censorship

Astrophysical evidence supporting Kerr black holes

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