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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 authors argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of space, only the behavior of matter in space and time.
Abstract: We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.
10 citations
01 Feb 1964
TL;DR: The non-existence of any physically acceptable solution of the Einstein-Maxwell equations can be identified as that of a charged infinite cylinder with a radial electrostatic field in this article.
Abstract: This letter establishes the non-existence of any physically acceptable solution of the Einstein-Maxwell equations which can be identified as that of a charged infinite cylinder with a radial electrostatic field.
10 citations
TL;DR: In this article, it was shown that the Newtonian potential that generates the static Schwarschild and Reissner-Nordstrom metrics also generates the NUT space metric from the class of Papapetrou stationary fields.
10 citations
TL;DR: Gravitational theories derived from an action principle where the Lagrange density is a power of the curvature scaler were investigated in this article, which predicts a bending of light of three-quarters of the value predicted by general relativity (n=1).
Abstract: Gravitational theories derived from an action principle where the Lagrange density is a power of the curvature scalerR
n
are investigated. For all values ofn the theories have the correct Newtonian limit and forn = 1 the same weak field solution, which predicts a bending of light of three-quarters of the value predicted by general relativity (n=1).
10 citations
TL;DR: In this article, the authors employ the principle of pre-established harmony between mathematics and physics to demonstrate that the original Einsteinian relativity, as opposed to the Minkowskian relativistically admissible 3-velocities that need not be parallel, is the legitimate formulation of special relativity whose time has returned.
Abstract: Soon after its appearance in 1905, the Einsteinian relativity with its relativistically admissible 3-velocities was recognized by Vladimir Varicak in 1908 as the realization in physics of the hyperbolic geometry of Bolyai and Lobachevski At the same time, however, during the years 1907–1909 Minkowski reformulated the Einsteinian relativity in terms of a space of 4-velocities that now bears his name As a result, the special theory of relativity that we find in the mainstream literature is not the one originally formulated by Einstein but, rather, the one reformulated by Minkowski Thus, in particular, one of the most powerful ideas of Einstein in 1905, the Einstein addition of relativistically admissible 3-velocities that need not be parallel, is unheard of in most texts on relativity physics Following our recently published book, Beyond the Einstein Addition, Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces [1], the aim of this article is to employ the principle of pre-established harmony between mathematics and physics to demonstrate that the original Einsteinian relativity, as opposed to the Minkowskian relativity, is the legitimate formulation of special relativity whose time has returned
10 citations