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Exact Solutions of Einstein's Field Equations
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A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.Abstract:
A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.read more
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The killing-yano tensor
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The Birkhoff theorem and string clouds
TL;DR: In this paper, the authors considered spherically symmetric space times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., ).
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Quantization of pure gravitational plane waves
TL;DR: In this article, the authors considered pure gravitational plane waves as a special case of spacetimes with two commuting spacelike Killing vector fields, and they introduced gauge-fixing and symmetry conditions that remove all non-physical degrees of freedom and ensure that the classical solutions are plane waves.
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Unpolarized radiative cylindrical spacetimes: trapped surfaces and quasilocal energy
TL;DR: In this paper, a formal derivation of Thorne's C-energy was presented based on a Hamiltonian reduction approach, which is a non-polynomial function of the Brown-York quasilocal energy.
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Taub’s plane-symmetric vacuum spacetime reexamined
TL;DR: In this paper, the gravitational properties of the only static plane-symmetric vacuum solution of Einstein's field equations without a cosmological term (Taub's solution) are presented: some already known properties (geodesics, weak field limit, and pertainment to the Schwarzschild family of spacetimes) are reviewed in a physically much more transparent way, as well as new results about its asymptotic structure, possible matchings, and the nature of the source are furnished.