Near horizon gravitational charges

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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.