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