Light-like shockwaves in scalar-tensor theories

TL;DR

This paper develops generalized junction conditions for scalar-tensor theories, specifically Brans-Dicke theory, describing how shockwaves and gravitational waves influence spacetime across null and non-null hypersurfaces.

Contribution

It introduces a novel formalism using a transverse vector for junction conditions in scalar-tensor theories, extending the Lanczos equation to include scalar field effects.

Findings

Derived generic junction conditions for Brans-Dicke theory.

Extended the Lanczos equation to scalar-tensor contexts.

Decomposed null hypersurface sources into density, current, and pressure.

Abstract

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.