Abbott-Deser energy in connection with Thirring's superpotentials

TL;DR

This paper explores the Abbott-Deser energy in curved spacetimes by linearizing Einstein's equations with a cosmological constant and integrating spin connections through differential forms.

Contribution

It introduces a novel approach to defining Abbott-Deser charges using spin connections and differential forms on curved backgrounds.

Findings

Reconstruction of Abbott-Deser charges with spin connection inclusion

Extension of energy definitions to curved backgrounds with cosmological constant

Enhanced understanding of gravitational energy in complex spacetimes

Abstract

We linearize vacuum Einstein field equations with a cosmological constant around a curved background to elaborate on the reconstruction of the Abbott-Deser charges and incorporate a spin connection into the definition using the algebra of differential forms on a given curved background spacetime.