Gravitational Memory and Compact Extra Dimensions

TL;DR

This paper develops a formalism to analyze gravitational memory effects in theories with extra dimensions, revealing how asymptotic symmetries and observable signals can encode properties of compact internal spaces.

Contribution

It introduces a generalized news tensor and a preferred gauge to study radiative modes and asymptotic symmetries in higher-dimensional theories with Ricci-flat internal spaces.

Findings

Extended BMS group includes internal space isometries

Memory effects linked to higher-dimensional gravitational radiation

Potential for gravitational wave observations to probe extra dimensions

Abstract

We develop a general formalism for treating radiative degrees of freedom near $\mathscr{I}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the BMS group to include angle-dependent isometries of the internal space. We apply this formalism to study memory effects, which are expected to be observed in future experiments, that arise from bursts of higher-dimensional gravitational radiation. We outline how measurements made by gravitational wave observatories might probe properties of the compact extra dimensions.