Asymptotic Symmetries of Rindler Space at the Horizon and Null Infinity

TL;DR

This paper explores the asymptotic symmetries of Rindler space at null infinity and the horizon, revealing finite and infinite-dimensional algebras depending on boundary conditions, with implications for conserved charges and symmetry representations.

Contribution

It systematically analyzes the asymptotic symmetry algebras of Rindler space, including cases with relaxed boundary conditions, and computes the associated conserved charges and their algebraic properties.

Findings

Finite-dimensional algebra at null infinity with standard boundary conditions.

Infinite-dimensional algebra at null infinity with relaxed boundary conditions.

Charges are finite, conserved, and form a trivial central extension.

Abstract

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.