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Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects

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Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects

dc.contributor.author	Lapiedra Civera, Ramón
dc.contributor.author	Morales Lladosa, Juan Antonio
dc.date.accessioned	2019-10-28T15:29:07Z
dc.date.available	2019-10-28T15:29:07Z
dc.date.issued	2019
dc.identifier.uri	https://hdl.handle.net/10550/71816
dc.description.abstract	We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is C1 class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac δ functions) discontinuities, the Dirac δ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the Einstein field equations can only exist in the sense of distributions. Then, we assume that the metric considered is C1 class everywhere and is a solution of the Einstein field equations in this sense. We explore the consequences of these two assumptions, and in doing so we derive the general conditions that constrain the jumps in the second partial derivatives across the boundary. The example of the Oppenheimer-Snyder metric is considered and some new results are obtained on it. Then, the formalism developed in this exploration is applied to a different situation, i.e., to a given generalization of the Einstein field equations for the case where the partial second derivatives of the metric exist but are not symmetric.
dc.language.iso	eng
dc.relation.ispartof	Physical Review D, 2019, vol. 100, num. 6, p. 064045-1-064045-10
dc.rights.uri	info:eu-repo/semantics/openAccess
dc.source	Lapiedra Civera, Ramón Morales Lladosa, Juan Antonio 2019 Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects Physical Review D 100 6 064045-1 064045-10
dc.subject	Gravitació
dc.subject	Relativitat general (Física)
dc.subject	Astrofísica
dc.title	Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects
dc.type	info:eu-repo/semantics/article
dc.date.updated	2019-10-28T15:29:07Z
dc.identifier.doi	https://doi.org/10.1103/PhysRevD.100.064045
dc.identifier.idgrec	134883