Asymptotic analysis of Einstein-{\AE}ther theory and its memory effects: the linearized case

TL;DR

This paper investigates the asymptotic behaviors, symmetries, and memory effects of linearized Einstein-e6ther theory, revealing similarities and new phenomena compared to general relativity, including vector and scalar mode memories.

Contribution

It provides a detailed analysis of asymptotic symmetries and memory effects in linearized Einstein-e6ther theory, highlighting new memory effects from vector and scalar modes.

Findings

All three modes have BMS-like symmetries.

Existence of subleading asymptotic symmetries.

Identification of new memory effects from vector and scalar modes.

Abstract

This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various multipolar moments. The suitable coordinate transformations are then determined, and the so-called pseudo-Newman-Unti coordinate systems are constructed for all radiative modes. In these coordinates, it is easy to identify the asymptotic symmetries. It turns out that all three kinds of modes possess the familiar Bondi-Metzner-Sachs symmetries or the extensions as in general relativity. Moreover, there also exist the \emph{subleading} asymptotic symmetries parameterized by a time-independent vector field on a unit 2-sphere. The memory effects are also identified. The tensor gravitational wave also excites similar displacement, spin, and center-of-mass memories to those in general relativity. New memory effects due to the vector and scalar modes exist. The subleading asymptotic symmetry is related to the (leading) vector displacement memory effect, which can be viewed as a linear combination of the electric-type and magnetic-type memory effects. However, the scalar memory effect seems to have nothing to do with the asymptotic symmetries at least in the linearized theory.