Near horizon gravitational charges

TL;DR

This paper explores how topological terms like Pontryagin and Gauss-Bonnet influence near horizon gravitational charges within the Newman-Penrose formalism, revealing novel features and contributions to the understanding of black hole symmetries.

Contribution

It demonstrates that topological terms significantly affect near horizon charges and can be derived from symplectic potential ambiguities, offering new insights into gravitational symmetries.

Findings

Topological terms alter near horizon gravitational charges.

Pontryagin and Gauss-Bonnet terms influence charge calculations.

Novel features emerge from topological contributions.

Abstract

In this paper, we study the near horizon symmetry and gravitational charges in the Newman-Penrose formalism. In particular we investigate the effect from topological terms. We find that the Pontryagin term and Gauss-Bonnet term have significant influence on the near horizon charges and bring interesting novel features. We show that the gravitational charge derived from a general class of topological terms including the Pontryagin term and Gauss-Bonnet term can be obtained from the ambiguities of the symplectic potential.