BransDicke theory in BondiSachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitationalwave memory effects
Abstract
Gravitationalwave 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, including its asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in BransDicke 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 BondiMetznerSachs group in general relativity. Because there is an additional polarization of gravitational waves in BransDicke theory, we compute the memory effects associated with this extra polarization (the socalled "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 breathingmodetype memory effects.
 Publication:

Physical Review D
 Pub Date:
 May 2021
 DOI:
 10.1103/PhysRevD.103.104026
 arXiv:
 arXiv:2007.13799
 Bibcode:
 2021PhRvD.103j4026T
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 Appendix added, section 2B modified, minor modifications to the introduction, matches published version