Gravitational-wave memory effects in the Damour-Esposito-Far\`ese extension of Brans-Dicke theory

TL;DR

This paper investigates gravitational-wave memory effects within the Damour-Esposito-Far extquoterightese extension of Brans-Dicke theory, highlighting subtle differences from general relativity and implications for future gravitational wave observations.

Contribution

It extends the Bondi-Sachs framework to this scalar-tensor theory, analyzing how additional scalar degrees of freedom influence memory effects and their potential observability.

Findings

Memory effects are similar in leading order to those in general relativity.

Differences in memory signals are second-order in the coupling parameter.

The scalar field evolution affects the time dependence of memory signals.

Abstract

Gravitational-wave memory effects are lasting changes in the strain and its time integrals. They can be computed in asymptotically flat spacetimes using the conservation and evolution equations in the Bondi-Sachs framework. Modified theories of gravity have additional degrees of freedom with their own asymptotic evolution equations; these additional fields can produce differences in the memory effects in these theories from those in general relativity. In this work, we study a scalar-tensor theory of gravity known as the Damour-Esposito-Far\`ese extension of Brans-Dicke theory. We use the Bondi-Sachs framework to compute the field equations in Bondi-Sachs form, the asymptotically flat solutions, and the leading gravitational-wave memory effects. Although Damour-Esposito-Far\`ese theory has additional nonlinearities not present in Brans-Dicke theory, these nonlinearities are subleading effects; thus, the two theories share many similarities in the leading (and some subleading) solutions to hypersurface equations, asymptotic symmetries, and types of memory effects. The conservation equations for the mass and angular momentum aspects differ between the two theories, primarily because of the differences in the evolution equation for the scalar field. This leads to differences in the time dependence of the gravitational-wave memory signals that are produced during the quasicircular inspiral of compact binaries. These differences, however, are of second-order in a small coupling parameter of these theories, which suggests that it would be challenging to use memory effects to distinguish between these two theories. Nevertheless, our results can be used to analyze and interpret memory effects from numerical-relativity simulations of binaries in this theory.