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Introduction to the mathematics of general relativity
About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.
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TL;DR: The evolution of BH binaries in vacuum spacetimes constitutes the two-body problem in general relativity as mentioned in this paper, and the solution of this problem in the framework of the Einstein field equations is a substantially more complex exercise than that of the dynamics of two point masses in Newtonian gravity, but also presents us with a wealth of new exciting physics.
Abstract: The evolution of black-hole (BH) binaries in vacuum spacetimes constitutes the two-body problem in general relativity. The solution of this problem in the framework of the Einstein field equations is a substantially more complex exercise than that of the dynamics of two point masses in Newtonian gravity, but it also presents us with a wealth of new exciting physics. Numerical methods are likely to be the only way to compute the dynamics of BH systems in the fully nonlinear regime and have been pursued since the 1960s, culminating in dramatic breakthroughs in 2005. Here we review the methodology and the developments that finally gave us a solution of this fundamental problem of Einstein's theory and discuss the breakthroughs' implications for the wide range of contemporary BH physics.
46 citations
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TL;DR: In this article, the relativistic expressions for the Abraham and Minkowski momenta, together with corresponding balance equations for an isotropic and homogeneous medium are derived.
46 citations
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TL;DR: In this paper, the problem of non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case.
Abstract: The problem tackled by B. K. Datta, [1] in a recent paper concerning non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case. A full classification of the possible motions is given.
46 citations
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TL;DR: In this paper, the authors apply the energy-momentum tensor to calculate energy, momentum and angular momentum of two different tetrad fields and show that the energy associated with one of them is consistent, while the other one does not show this consistency.
Abstract: We apply the energy-momentum tensor to calculate energy, momentum and angular-momentum of two different tetrad fields. This tensor is coordinate independent of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR). The spacetime of these tetrad fields is the charged dilaton. Our results show that the energy associated with one of these tetrad fields is consistent, while the other one does not show this consistency. Therefore, we use the regularized expression of the gravitational energy-momentum tensor of the TEGR. We investigate the energy within the external event horizon using the definition of the gravitational energy-momentum.
46 citations