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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 article, the authors presented a method of obtaining varieties of new exact solutions representing static balls of perfect fluid in general relativity, which indicated the possibility of constructing a plethora of new physically significant models of relativistic stellar interiors with equations of state fairly applicable to the case of extremely compressed stars.
Abstract: In this paper we present a method of obtaining varieties of new classes of exact solutions representing static balls of perfect fluid in general relativity. A number of previously known classes of solutions has been rediscovered in the process. The method indicates the possibility of constructing a plethora of new physically significant models of relativistic stellar interiors with equations of state fairly applicable to the case of extremely compressed stars. To emphasize our point we have derived two new classes of solutions and discussed their physical importance. From the solutions of these classes we have constructed three causal interiors out of which in two models the outward march of pressure, density, pressure-density ratio and the adiabatic sound speed is monotonically decreasing.
12 citations
TL;DR: The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years as discussed by the authors, following the perspective of deformations, while staying within the framework of Lie algebra, and explore systematically the resulting physical interpretations.
Abstract: The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie algebra, we implement explicitly a simple linear realization of the relativity symmetry, and explore systematically the resulting physical interpretations. Some suggestions we make may sound radical, but are arguably natural within the context of our formulation. Our work may provide a new perspective on the subject matter, complementary to the previous approach(es), and may lead to a better understanding of the physics.
12 citations
TL;DR: In this article, a tensor formulation of synchronization transformations within special relativity is given to bridge the gap between some philosophical discussions (e.g., by Grunbaum and Winnie) and the analyses given by physicists.
Abstract: We give a tensor formulation of synchronization transformations within special relativity in order to bridge the gap between some philosophical discussions (e.g., by Grunbaum and Winnie) and the analyses given by physicists (e.g., Moller). As an application, we discuss a physical interpretation of the duality between covariant and contravariant indices in the tensor formulation.
12 citations
12 citations
TL;DR: In this paper, the distance dependence of gravity is found in Newtonian universes with any number n of space dimensions and two independent derivations given are based either on (i) requiring that a (hyper) spherical mass gravitate as if all its mass were concentrated at its center, or (ii) using the field equations of general relativity with the cosmological constant Λ.
Abstract: The distance dependence of gravity is found in Newtonian universes with any number n of space dimensions. Two independent derivations given are based either on (i) requiring that a (hyper) spherical mass gravitate as if all its mass were concentrated at its center, or (ii) using the field equations of general relativity with the cosmological constant Λ. Both approaches lead to identical results. The gravity field at distance r from a point mass has two parts, one going as r1−n, the other as r, i.e., Hooke’s law. The Hookian field obeys a novel form of Gauss’s (flux) law, and is closely related to Λ. The simple mechanical interpretation which emerges gives insight into the meaning of Λ and helps counteract certain prevalent misconceptions.
11 citations