Light-like shockwaves in scalar-tensor theories

Both electromagnetic shock-waves and gravitational waves propagate with the speed of light. If they carry significant energy-momentum, this will change the properties of the space-time they propagate through. This can be described in terms of the junction conditions between space-time regions separa...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: Racskó, Bence, László Árpád Gergely
Format: Article
Language:English
Subjects:
Gravitation theory
Gravitational waves
Hyperspaces
Light speed
Mathematical analysis
Momentum
Relativity
Shock waves
Spacetime
Tensors
Online Access:Get full text
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Summary:Both electromagnetic shock-waves and gravitational waves propagate with the speed of light. If they carry significant energy-momentum, this will change the properties of the space-time they propagate through. This can be described in terms of the junction conditions between space-time regions separated by a singular, null hypersurface. We derived generic junction conditions for Brans-Dicke theory in the Jordan frame, exploring a formalism based on a transverse vector, rather than normal, which can be applied to any type of hypersurfaces. In the particular case of a non-null hypersurface we obtain a generalised Lanczos equation, in which the jump of the extrinsic curvature is sourced by both the distributional energy-momentum tensor and by the jump in the transverse derivative of the scalar. In the case of null hypersurfaces, the distributional source is decomposed into surface density, current and pressure. The latter however ought to vanish by virtue of the scalar junction condition.
ISSN:2331-8422
DOI:10.48550/arxiv.2006.13010