Gravitational memory effects and Bondi-Metzner-Sachs symmetries in scalar-tensor theories

Abstract

The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetries of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinite dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors in the scalar-tensor theory. The supertranslation relates the vacua in the tensor sector, while in the scalar sector, it is the Lorentz transformation that transforms the vacua to each other. So there are the tensor memory effects similar to the ones in general relativity, and the scalar memory effect, which is new. The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively.

Gravitational memory effects in Brans‐Dicke theory

“…The asymptotic symmetries, or BMS symmetries, are diffeomorphisms that preserve the boundary conditions defined in the previous section. An infinitesimal asymptotic symmetry a is the easiest to be determined by solving the following conditions (Hou & Zhu, 2020b):…”

“…Φ for some function Φ(x A ), so N AB = 0 (Hou & Zhu, 2020b). This kind of state can be transformed by a supertranslation to a state withĉ…”

“…The flux-balance laws provide constraints on the memory effects. For more details, please refer to Hou & Zhu (2020a), Hou & Zhu (2020b) and Tahura et al (2020). This work mainly discusses the displacement memories in the tensor and the scalar sectors.…”

Gravitational breathing memory and dual symmetries

“…A convenient setup for this analysis is the Bondi-Sachs formalism, in which the fields are expanded in negative powers of the distance, and the equations are solved order by order. A detailed analysis of the Brans-Dicke theory in the Bondi-Sachs formalism was performed recently in [32,34],…”

“…The BMS symmetries and their balance equations in BD theory were studied in detail in [32][33][34]. These balance equations determine the memory effects in tensorial modes of the GW.…”