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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: In this paper, the pseudo-local gravitoelectromagnetic stress-energy tensor for an arbitrary gravitational field within the framework of general relativity was studied and it was shown that there exists a current of gravitational energy around a rotating mass.
Abstract: We study the pseudo-local gravitoelectromagnetic stress-energy tensor for an arbitrary gravitational field within the framework of general relativity. It is shown that there exists a current of gravitational energy around a rotating mass. This gravitational analogue of the Poynting flux is evaluated for certain classes of observers in the Kerr field.
43 citations
Book•
01 Jan 2005
TL;DR: Tensors, Relativity, and Cosmology, Second Edition as discussed by the authors combines tensors, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations.
Abstract: Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe.
43 citations
TL;DR: In this paper, Bertschinger and Hamilton derived equations for the electric and magnetic parts of the Weyl tensor for cold dust for both General Relativity and Newtonian theory.
Abstract: In an interesting recent paper on the growth of inhomogeneity through the effect of gravity [1], Bertschinger and Hamilton derive equations for the electric and magnetic parts of the Weyl tensor for cold dust for both General Relativity and Newtonian theory. Their conclusion is that both in General Relativity and in Newtonian theory, in general the magnetic part of the Weyl tensor does not vanish, implying that the Lagrangian evolution of the fluid is not local. We show here that the `Newtonian' theory discussed by them is in fact not Newtonian theory {\it per se}, but rather a plausible relativistic generalisation of Newtonian theory. Newtonian cosmology itself is highly non-local irrespective of the behaviour of the magnetic part of the Weyl tensor; in this respect the Bertschinger-Hamilton generalisation is a better theory.
43 citations
TL;DR: In this article, a new exact solution of the field equations with the energy-momentum tensor of a perfect fluid is given, which can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure.
Abstract: A new exact solution of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. This solution can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure. The fluid rotates rigidly; the equation of state is epsilon +3p=constant. The solution is of Petrov type D and admits a maximal group G2 of motions.
42 citations
42 citations