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Special relativity (alternative formulations)
About: Special relativity (alternative formulations) is a research topic. Over the lifetime, 3102 publications have been published within this topic receiving 55015 citations.
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TL;DR: In this paper, a mathematical theory of nonlinear generalized functions based on Colombeau algebras is described and applied in general relativity, and it is shown that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations.
Abstract: We review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using distribution theory but require a more general concept. We describe a mathematical theory of nonlinear generalized functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations.
166 citations
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TL;DR: In this paper, it was shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR), which is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2 + 1 gravity found by Matschull and Welling and the corresponding DSR algebra.
Abstract: It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.
162 citations
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TL;DR: In this article, the Einstein-Maxwell field equations in the presence of one Killing vector are shown to possess covariance under an eight-parameter group of linear substitutions in the field variables.
Abstract: The Einstein‐Maxwell field equations in the presence of one Killing vector are shown to possess covariance under an eight‐parameter group of linear substitutions in the field variables. This internal symmetry group is isomorphic to SU(2,1). Three of the degrees of freedom correspond to gage transformations, but the remaining ones allow us to generate a five‐parameter family of solutions given a single solution.
159 citations
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158 citations
01 Jan 2016
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151 citations