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

We consider a globally hyperbolic, stationary spacetime containing a black hole but no white hole. We assume, further, that the event horizon, N , of the black hole is a Killing horizon with compact cross-sections. We prove that if surface gravity is non-zero constant throughout the horizon one can globally extend such a spacetime so that the image of N is a proper subset of a regular bifurcate...