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

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 in an expansion in inverse luminosity distance; 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. When used to compute the time dependence of the gravitational-wave memory signals from quasicircular inspirals of binary neutron stars and black-hole--neutron-star binaries, they give rise to new features that are of second-order in a small coupling parameter in this theory. The observational bound that the coupling is small suggests that it would be challenging to use memory effects during the inspiral to distinguish between Brans-Dicke and Damour-Esposito-Far\`ese theories. Nevertheless, these results can be used to analyze and interpret memory effects from numerical-relativity simulations of binaries in this theory.