A modified Lie algebra based approach and its application to asymptotic symmetries on a Killing horizon
Abstract
We develop a new approach to find asymptotic symmetries in general relativity by modifying a Lie algebra based approach proposed in Ref.~\cite{tomitsuka2021}. The authors in Ref.~\cite{tomitsuka2021} proposed an algorithmic protocol to investigate asymptotic symmetries. In particular, their guiding principle help us to find a nonvanishing charge which generates an infinitesimal diffeomorphism. However, in order to check the integrability condition for the charges, it is required to solve differential equations to identify the integral curve of vector fields, which is usually quite hard. In this paper, we provide a sufficient condition of the integrability condition which can be checked without solving any differential equations, avoiding difficulties in the approach in Ref.~\cite{tomitsuka2021}. As a demonstration, we investigate the asymptotic symmetries on a Killing horizon and find the new asymptotic symmetries. In the case of a 4dimensional spacetime with a spherical Killing horizon, we show that the algebra of the corresponding charges is a central extension of the algebra of vector fields.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.04807
 Bibcode:
 2021arXiv211004807T
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 28 pages, 1 figures