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In this paper, we study the linearized gravity theory in the near horizonregion of the Schwarzschild black hole in four dimensional spacetime. Under theNewman-Unti gauge, we derive the most general near horizon symmetry andsolution space without any near horizon fall-off condition. There are fourtowers of surface charges that are generic functions on the horizon associatedto the near horizon symmetry. With suitable near horizon fall-off conditions,we reveal a soft graviton theorem from the Ward identity of the near horizonsupertranslation in both coordinates space and momentum space.

Near horizon linearized gravity and soft theorem