A Lie algebra based approach to asymptotic symmetries in general relativity

Abstract

Asymptotic symmetries of black hole spacetimes have received much attention as a possible origin of the Bekenstein–Hawking entropy in black hole thermodynamics. In general, it takes hard efforts to find appropriate asymptotic conditions on a metric and a Lie algebra generating the transformation of symmetries with which the corresponding charges are integrable. We here propose an alternative approach to construct building blocks of asymptotic symmetries of a given spacetime metric. Our algorithmic approach may make it easier to explore asymptotic symmetries in any spacetime than in conventional approaches. As an explicit application, we analyze the asymptotic symmetries on Rindler horizon. We find a new class of symmetries related with dilatation transformations in time and in the direction perpendicular to the horizon, which we term superdilatations.