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

arXiv comment126 Pages, 13 Figures, 360 References

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Cited by in corpus (34)

• Homogeneous Plane Waves
• Boost-rotation symmetric spacetimes - review
• Gravitating discs around black holes
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Accelerated sources in de Sitter spacetime and the insufficiency of retarded fields
• On General Solutions of Einstein Equations
• Static fluid cylinders and their fields: global solutions
• Hairy Taub-NUT/Bolt-AdS solutions in Horndeski theory
• Co-accelerated particles in the C-metric
• Fields of accelerated sources: Born in de Sitter
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• Einstein equations: exact solutions
• Some high-frequency gravitational waves related to exact radiative spacetimes
• Time-Periodic Solutions of the Einstein's Field Equations II
• Morgan-Morgan-NUT disk space via the Ehlers transformation
• Einstein-Rosen Waves and the Geroch Group
• Nonholonomic Ricci Flows: Exact Solutions and Gravity
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Weyl metrics and the generating conjecture
• The Newtonian limit of spacetimes for accelerated particles and black holes
• Construction and application of variations on the cylindrical gravitational waves of Weber, Wheeler, and Bonnor
• Accelerating electromagnetic magic field from the C-metric
• Gauged motion in general relativity and in Kaluza-Klein theories
• Gauge-invariant Hamiltonian dynamics of cylindrical gravitational waves
• Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes
• Lightlike sets with applications to the rigidity of null geodesic incompleteness
• Prolegomena to any future Quantum Gravity
• The Newtonian limit of spacetimes describing uniformly accelerated particles
• Reciprocal NUT spacetimes
• Breaking Generalized Covariance, Classical Renormalization and Boundary Conditions from Superpotentials
• Plane Waves and Vacuum Interpolation
• On the splitting problem for Lorentzian manifolds with an $\mathbb{R}$-action with causal orbits
• Time-periodic universes
• A Proof for a Theorem of Wald in Arbitrary Dimensions