A Lie algebra based approach to asymptotic symmetries in general relativity

TL;DR

This paper introduces an algebraic method based on Lie algebras to systematically identify asymptotic symmetries in spacetime metrics, demonstrated through analysis of Rindler horizons, revealing new symmetries called superdilatations.

Contribution

It proposes an algorithmic Lie algebra-based approach to construct asymptotic symmetries, simplifying the exploration process compared to traditional methods.

Findings

Identified a new class of symmetries called superdilatations.

Applied the method to Rindler horizons successfully.

Revealed symmetries related to dilatation transformations.

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.