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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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Conformal geometry of flows in n dimensions
Ivor Robinson,Andrzej Trautman +1 more
TL;DR: In this paper, a flow is defined to be conformally geodesic if it preserves the distribution of vector spaces orthogonal to the lines of the flow, and it is shear-free if, moreover, it preserves conformal structure on these vector spaces.
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Solutions to the Field Equations and the Deceleration Parameter
Sunil D. Maharaj,R. Naidoo +1 more
TL;DR: In this paper, a form for the Hubble parameter was used to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant, which is consistent with alternate theories of gravity by considering the scalar-tensor theory of Lau and Prokhovnik with a 0 Robertson-Walker background.
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Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions
José Luis Jaramillo,Rodrigo Panosso Macedo,Rodrigo Panosso Macedo,Philipp Moesta,Luciano Rezzolla +4 more
TL;DR: In this paper, the authors focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [L. Rezzolla, R. Macedo, P. Moesta, and L. L. Jaramillo, 2010] with Robinson-Trautman spacetimes.
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Teleparallel killing vectors of the einstein universe
Muhammad Sharif,M. Jamil Amir +1 more
TL;DR: In this article, the Lie derivative of a second rank tensor is defined in the context of the teleparallel theory of gravity and also extended to general tensors of rank p + q. This definition is then used to find the Killing vectors of the Einstein universe.
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Braneworld cosmological models with anisotropy
TL;DR: In this article, a family of Bianchi braneworlds with anisotropic stress on the brane was constructed by solving the Weyl tensor equations in the bulk.