Manifold invariants affect dynamics in ADS gravity

TL;DR

This paper investigates how manifold invariants influence the dynamics in Anti-de Sitter (ADS) gravity by analyzing the Holst action with a negative cosmological constant and its associated surface terms.

Contribution

It demonstrates that surface terms in ADS gravity, related to Euler and Pontryagin densities, modify Noether charges and are essential for the action's finiteness and differentiability.

Findings

Surface terms correspond to Euler and Pontryagin densities.

These terms alter the Noether charges in ADS gravity.

The action becomes finite and well-defined with these modifications.

Abstract

The first-order Holst action with negative cosmological constant is rendered finite by requiring functional differentiability on the configuration space of tetrads and connections. The surface terms that arise in the action for ADS gravity are equivalent to the Euler and Pontryagin densities with fixed weight factors; these terms modify the Noether charges that arise from diffeomorphism invariance of the action.