Exploring the Kleinian horizons

TL;DR

This paper investigates the near-horizon structure of self-dual black holes in Klein space, revealing infinite-dimensional symmetries and extending the understanding of asymptotic symmetries in this context.

Contribution

It extends the analysis of asymptotic symmetries to self-dual black holes in Klein space, identifying boundary conditions, symmetry algebra, and conserved charges.

Findings

Near the horizons, the geometry exhibits supertranslation and superrotation symmetries.

The symmetry algebra is infinite-dimensional and the charges are integrable.

The results connect to recent studies on self-dual black holes in Klein space.

Abstract

Self-dual black holes in (2,2) signature spacetime -- Klein space -- have recently attracted interest in the context of celestial holography. Motivated by this development, we investigate the structure of spacetime near the horizons of these solutions. Focusing on the self-dual Schwarzschild-Taub-NUT solution, we demonstrate that, near the Kleinian horizons, the geometry exhibits a local infinite-dimensional symmetry generated by supertranslations and superrotations. Establishing this result requires refining and extending earlier analyses of asymptotic symmetries near null surfaces. We formulate the appropriate boundary conditions, derive the infinite-dimensional algebra underlying the local symmetries, and compute the associated Noether charges, finding them to be integrable. Finally, we discuss the connection of our findings to recent observations in the literature regarding self-dual black holes in Klein space, including the diffeomorphism relating static and stationary solutions.