Balance flux laws beyond general relativity

TL;DR

This paper extends the concept of flux balance laws from general relativity to a broad class of alternative theories of gravity, providing a systematic framework for high-precision gravitational tests.

Contribution

It derives general flux laws for diffeomorphism-invariant theories beyond general relativity using covariant phase space formalism, including Horndeski theories, and compares different approaches.

Findings

Derived flux laws for Horndeski theories.

Validated flux laws against Brans-Dicke gravity.

Compared flux laws with Isaacson approach.

Abstract

Balance flux laws of asymptotic symmetries in general relativity provide fully non-perturbative constraint equations on gravitational strain. They have proven useful for constructing numerical gravitational waveforms and for characterizing gravitational memory. As the precision of current and future detectors continues to improve, such constraints become increasingly important for high-precision tests of gravity, including searches for deviations from general relativity. This motivates a systematic understanding of analogous balance laws in theories beyond general relativity. In this work, we investigate the existence and structure of flux laws at null infinity in diffeomorphism-invariant extensions of general relativity. Our analysis is based on the covariant phase space formalism and the definition of conserved quantities, as presented by Wald and Zoupas. For a particularly relevant class of Horndeski theories, we derive a general expression for the flux and formulate the corresponding balance equation via the associated non-conserved charges. We cross-check our general results by comparing them with previous studies of Brans-Dicke gravity. Furthermore, we demonstrate that the employed methods extend straightforwardly to a broader class of diffeomorphism-invariant theories. The null part of the resulting flux laws associated with null memory is compared with and validated against the alternative derivation based on the Isaacson approach to gravitational radiation. Beyond the specific results obtained, this work is intended to serve as a practical guide for computing balance laws in generic diffeomorphism-invariant theories of gravity and paves the way for an in-depth comparison between the Isaacson approach and the covariant phase space formalism.