The homotopy momentum map of general relativity

TL;DR

This paper demonstrates that the action of spacetime vector fields in general relativity admits a homotopy momentum map, extending Noether's theorem to a broader algebraic framework involving $L_$-algebras.

Contribution

It introduces a homotopy momentum map for general relativity, generalizing the classical Noether current map to an $L_$-algebra morphism.

Findings

Homotopy momentum map extends Noether's theorem in GR.

Establishes a morphism of $L_$-algebras for spacetime symmetries.

Provides a new algebraic structure for conserved quantities in GR.

Abstract

We show that the action of spacetime vector fields on the variational bicomplex of general relativity has a homotopy momentum map that extends the map from vector fields to conserved currents given by Noether's first theorem to a morphism of $L_\infty$-algebras.