Diffeomorphism symmetries near a timelike surface in black hole spacetime

Recently symmetries of gravity and gauge fields in the asymptotic regions spacetime have been shown to play vital role their low energy scattering phenomena. Further, for black hole spacetime, near horizon symmetry has observed possible understanding underlying degrees freedom thermodynamic behaviour horizon. Following similar idea, this paper, we analyzed associated algebra a timelike surface which is situated at any arbitrary radial position embedded spacetime. In paper considered both Schwarzschild Kerr spacetimes. The families hypersurfaces with constant coordinate (outside horizon) these spacetimes nature divide space into two distinct regions. turned out be reminiscent Bondi-Metzner-Sach (BMS) symmetry, found null infinity.