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Four-force
About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.
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TL;DR: In this paper, the conservation laws based upon the existence of curvature and Ricci collineations are investigated and the results given recently by Katzin, Levine and Davis are reinterpreted and generalized.
Abstract: The conservation laws based upon the existence of curvature and Ricci collineations are investigated and the results given recently by Katzin, Levine and Davis are reinterpreted and generalized. The concept of a ‘Maxwell collineation’ is introduced and corresponding conservation laws are found.
29 citations
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TL;DR: In this article, given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, the authors show how to construct a new solution of the constraints which is itself asymptonically Euclidian, and which contains specified sub-regions of each of the given solutions.
Abstract: Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions of each of the N given solutions. This generalizes earlier work which handled the time-symmetric case, thus providing a construction of large classes of initial data for the many body problem in general relativity.
29 citations
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TL;DR: In this paper, Born's reciprocal general relativity theory in curved space-time was extended to the curved phase-space scenario, which requires the introduction of a complex Hermitian metric, torsion and nonmetricity.
Abstract: We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space–time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space–time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario.
29 citations
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01 Jan 198028 citations
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TL;DR: In this article, the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor are discussed and algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form are presented.
Abstract: This is the first in a series of papers concerning a project to set up a computer database of exact solutions in general relativity which can be accessed and updated by the user community. In this paper, we briefly discuss the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor. We then present algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form.
28 citations