Conserved charges in Chern-Simons modified theory and memory effects

TL;DR

This paper investigates conserved charges and memory effects at null infinity in Chern-Simons modified gravity, revealing similarities to Brans-Dicke theory and describing scalar memory via large gauge transformations.

Contribution

It extends the analysis of asymptotic symmetries and conserved charges to Chern-Simons modified gravity, including tensor and scalar memory effects, using conformal completion and dual formalism.

Findings

Conserved charges resemble those in Brans-Dicke theory.

Scalar memory is characterized by large gauge transformations of a dual 2-form field.

Memory effects are constrained by flux-balance laws.

Abstract

In this work, conserved charges and fluxes at the future null infinity are determined in the asymptotically flat spacetime for Chern-Simons modified gravity. The flux-balance laws are used to constrain the memory effects. For tensor memories, the Penrose's conformal completion method is used to analyze the asymptotic structures and asymptotic symmetries, and then, conserved charges for the Bondi-Metzner-Sachs algebra are constructed with the Wald-Zoupas formalism. These charges take very similar forms to those in Brans-Dicke theory. For the scalar memory, Chern-Simons modified gravity is rewritten in the first-order formalism, and the scalar field is replaced by a 2-form field dual to it. With this dual formalism, the scalar memory is described by the vacuum transition induced by the large gauge transformation of the 2-form field.