Probing Gravity -- Fundamental Aspects of Metric Theories and their Implications for Tests of General Relativity

TL;DR

This paper reviews the implications of the Einstein equivalence principle on metric theories of gravity, explores gravitational wave energy-momentum and memory effects, and generalizes Isaacson's approach to include a wide class of theories for future experimental tests.

Contribution

It provides a unified framework for understanding gravitational wave memory effects across various metric theories of gravity, extending Isaacson's approach.

Findings

Memory effects can be derived for a broad class of metric theories.

Unified understanding of null and ordinary memory effects.

Implications for future gravitational wave measurements.

Abstract

Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of gravity. The resulting space of metric theories of gravity may address open conceptual and observational puzzles through a wealth of effects beyond general relativity, whose traces can be searched for within today's and tomorrow's gravitational testing grounds. Above all, we offer a generic metric theory generalization of Isaacson's approach to the leading-order field equations of physical perturbations with a well-defined notion of energy-momentum carried by the gravitational waves. Within this framework, we identify the backreaction of the Isaacson energy-momentum flux onto the background spacetime with the displacement memory effect that induces a permanent distortion of space after the passage of a gravitational wave. This effect is a well-known prediction of GR whose dominant contribution captures its inherent non-linear nature, manifest in the ability of gravity to gravitate. However, the novel interpretation of memory as naturally arising within the Isaacson approach to gravitational waves comes with two main advantages. Firstly, it allows for a unified understanding of both the null and the ordinary memory effect, which are respectively sourced by unbound energy fluxes that do and do not reach asymptotic null infinity. Secondly, and most importantly, this approach allows for a consistent derivation of the memory formula for a large class of metric theories with considerable lessons to be learned for upcoming future measurements of the memory effect.