Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory

TL;DR

This work analyzes gravitational-wave memory in the Damour-Esposito-Farèse scalar-tensor extension of Brans-Dicke theory using the Bondi-Sachs framework. It demonstrates that the leading tensor memory structure matches BD/GR but deviations arise in the time evolution of the scalar field, particularly at subleading orders, yielding memory signals with theory-specific time dependence. The memory fluxes retain the same formal forms as in BD when expressed through Wald-Zoupas charges and fluxes, with differences entering at second order in the DEF coupling parameter ${f B_0}$ via the evolution of $oldsymbol{ extlambda_2}$ and related mass/ angular-momentum definitions. The results establish a pathway to interpret memory signals from DEF numerical-relativity simulations and to contrast them with BD predictions, while highlighting that memory-based discrimination between these theories remains challenging without high-precision NR data near merger.

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-Farèse 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-Farèse 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.