Singular Hypersurfaces in Scalar-Tensor Theories of Gravity

TL;DR

This paper develops a formalism for analyzing singular hypersurfaces in scalar-tensor gravity theories, deriving general junction equations applicable to various hypersurface types and applying them to specific spacetime examples.

Contribution

It introduces a distributional and intrinsic approach to junction conditions in scalar-tensor gravity, covering lightlike shells and diverse hypersurface configurations.

Findings

Derived general junction equations for all hypersurface types.

Applied formalism to static spherically symmetric spacetimes.

Analyzed planar domain walls and impulsive waves.

Abstract

We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike shells and write the general equations of evolution for these objects. We apply this formalism to various examples in static spherically symmetric spacetimes, and to the study of planar domain walls and plane impulsive waves.