Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitational-wave memory effects

TL;DR

This paper explores gravitational-wave memory effects in Brans-Dicke theory, analyzing asymptotic symmetries and the unique breathing mode, revealing new memory phenomena beyond those in general relativity.

Contribution

It derives the asymptotic symmetry group in Brans-Dicke theory and investigates the associated memory effects, including the novel breathing mode memory.

Findings

The asymptotic symmetry group matches the BMS group of GR.

Breathing mode produces a uniform expansion or contraction of observers.

Additional memory effects depend on initial and final nonradiative regions.

Abstract

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.