Kundt geometries and memory effects in the Brans-Dicke theory of gravity

TL;DR

This paper investigates gravitational memory effects in Brans-Dicke scalar-tensor theory using newly introduced Kundt spacetimes, revealing how scalar field and parameter variations influence memory phenomena compared to general relativity.

Contribution

It introduces novel Kundt geometries in Brans-Dicke theory and analyzes their role in gravitational memory effects, highlighting differences from general relativity.

Findings

Memory effects depend on the Brans-Dicke parameter $$ and scalar field profile.

Exact solutions are found for the special case $=-2$, showing clear displacement memory.

Numerical geodesic analysis supports the theoretical findings on memory effects.

Abstract

Memory effects are studied in the simplest scalar-tensor theory, the Brans--Dicke (BD) theory. To this end, we introduce, in BD theory, novel Kundt spacetimes (without and with gyratonic terms), which serve as backgrounds for the ensuing analysis on memory. The BD parameter $\omega$ and the scalar field ($\phi$) profile, expectedly, distinguishes between different solutions. Choosing specific localised forms for the free metric functions $H'(u)$ (related to the wave profile) and $J(u)$ (the gyraton) we obtain displacement memory effects using both geodesics and geodesic deviation. An interesting and easy-to-understand exactly solvable case arises when $\omega=-2$ (with $J(u)$ absent) which we discuss in detail. For other $\omega$ (in the presence of $J$ or without), numerically obtained geodesics lead to results on displacement memory which appear to match qualitatively with those found from a deviation analysis. Thus, the issue of how memory effects in BD theory may arise and also differ from their GR counterparts, is now partially addressed, at least theoretically, within the context of this new class of Kundt geometries.