Near horizon gravitational charges

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.