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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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Covariantly constant tensors and holonomy structure in general relativity
TL;DR: In this article, the authors give a comprehensive discussion of space times that admit vector fields or skew-symmetric tensor fields which are covariantly constant or recurrent. And the relationship between such space times M and their holonomy group is given.
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Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: The regular case
TL;DR: In this paper, numerical solutions of the Einstein-Yang-Mills equations with a negative cosmological constant are constructed, and axially symmetric solutions approach asymptotically the anti-de Sitter spacetime and are regular everywhere.
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Non-newtonian behavior in weak field general relativity for extended rotating sources
Herbert Balasin,Daniel Grumiller +1 more
TL;DR: In this article, an exact stationary axially symmetric solution to the four-dimensional Einstein equations with corotating pressureless perfect fluid sources is studied, and a particular solution with an approximately flat rotation curve is discussed.
Journal ArticleDOI
Hamiltonian evolution and quantization for extremal Black holes.
Claus Kiefer,Jorma Louko +1 more
TL;DR: In this article, two distinct ways of including extremal black holes in a Lor- entzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory are presented.
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Lorentzian manifolds isometrically embeddable in L^N
Olaf L. Müller,Miguel Sánchez +1 more
TL;DR: In this paper, it was shown that any globally hyperbolic spacetime can be isometrically embedded in some Lorentz-Minkowski space L^N. This is proven by the construction of a smooth time function whose gradient is bounded away from zero.