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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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13 citations
TL;DR: In this paper, the equivalence between the loop space approach and the discrete Regge description of general relativity is pointed out, and a generalisation to the (3+1)-dimensional spacetime describing a cosmic string is given.
Abstract: Describes Einstein gravity in (2+1)-dimensional, spacetime, with point particle sources, using the loop variable approach. In this case the author points out the equivalence between the loop space approach and the discrete Regge description of general relativity. A generalisation to the (3+1)-dimensional spacetime describing a cosmic string is given.
13 citations
13 citations
TL;DR: In this paper, Bianchi VI spacetime is reduced to Bianchi types VI0-V-III-I and exact solutions for the universes indefinitely expanding with constant mean deceleration parameter are discussed for each Bianchi type.
Abstract: We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.
13 citations
TL;DR: In this article, a method to find the exact solutions of the Einstein's field equations by using which they construct time-periodic solutions was developed, and some new physical phenomena, such as the time periodic event horizon, were found.
Abstract: In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new physical phenomena, such as the time-periodic event horizon, are found. The applications of these solutions in modern cosmology and general relativity are expected.
13 citations