Constraining superluminal Einstein-\AE{}ther gravity through gravitational memory

TL;DR

This paper calculates gravitational displacement memory in Einstein-Aether gravity, revealing that superluminal propagation leads to unbounded memory effects, which likely exclude superluminal parameter regions.

Contribution

First direct computation of gravitational memory in a metric theory with a nontrivial asymptotic vector field, extending understanding of gravitational memory in Einstein-Aether gravity.

Findings

Superluminal scalar and vector waves cause unbounded memory build-up.

Results suggest superluminal parameter space is likely excluded.

Memory effects depend on wave propagation speeds.

Abstract

Every emission of radiation in gravity also includes a nonwavelike component that leaves a permanent change in proper distances of the spacetime it travels through. This phenomenon is known as gravitational displacement memory. Building up on a recently developed computation framework that harnesses Isaacson's insights on a fundamental definition of gravitational waves, we compute the leading displacement memory formula in Einstein-Aether gravity. Our analysis represents the first direct calculation of gravitational memory in a metric theory with nontrivial asymptotic vector field value. We find that an emission of scalar and vector aether waves at a propagation speed greater than the speed of tensor radiation features unprotected causal directions with a priori unbound memory build-up. Based on the results and the existing constraint of luminally propagating tensor waves, we conjecture a stringent exclusion of the superluminal parameter space of Einstein-Aether gravity.