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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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Affine collineations in general relativity and their fixed point structure
TL;DR: A general discussion of affine vector fields (collineations) in space-time is given following a previous article by Hall and da Costa as discussed by the authors, where the impossibility of reducing an affine algebra containing proper vector fields to homothetic or Killing vector fields, by means of a change of compatible metric, is demonstrated.
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Rotating black holes with an anisotropic matter field
TL;DR: In this article, a family of new rotating black hole solutions to Einstein's equations that generalizes the Kerr-Newman spacetime to include an anisotropic matter was presented. And the properties of the black hole were analyzed in detail including thermodynamics.
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The role of the ergosphere in the Blandford–Znajek process
TL;DR: In this paper, the authors studied the evolution of force-free electromagnetic fields on regular spacetimes with an ergosphere, which are generated by rapidly rotating stars, and showed that the radiated energy depends exponentially on the compactness of the star.
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Gravitational Collapse of Self-Similar Perfect Fluid in 2+1 Gravity
TL;DR: In this paper, perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given.
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Vacuum Friedmann Model in Self-Creation Cosmology
TL;DR: In this article, the self-creation theory of gravitation is solved for a vacuum with the aid of a space-time metric of Friedmann, and some physical properties of the solution are discussed.