Adjoint L-Infinity Actions and Conserved Charges in GR

TL;DR

This paper introduces a novel algebraic method using $L_ abla$-algebras to compute conserved charges in Einstein--Cartan--Palatini gravity, demonstrated through black hole entropy calculations.

Contribution

It develops a new $L_ abla$-algebra framework for conserved charges in gravity, extending the algebraic understanding of symmetries and charges.

Findings

Computed conserved currents and charges for Einstein--Cartan--Palatini gravity.

Applied the method to derive the Schwarzschild black hole entropy.

Proved a new algebraic result on higher adjoint actions of $L_ abla$-algebras.

Abstract

In this work we compute the conserved currents and charges associated to the action of an infinitesimal isometry (Killing field) in Einstein--Cartan--Palatini gravity. We offer a new approach to these quantities through the formalism of $L_\infty$-algebras and the work of \'{C}iri\'{c}, Giotopoulos, Radovanovi\'{c}, and Szabo, and Costello and Gwilliam. We demonstrate our approach by computing the entropy of the Schwarzchild black hole. Along the way, we prove a purely algebraic result about the existence and utility of a higher (a full $\infty$) version of the adjoint action of an $L_\infty$-algebra.