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  • Open Access

Exploring the Kleinian horizons

Gaston Giribet1, Juan Laurnagaray2, Bryan Malpartida2, and Pedro Schmied2

  • 1Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York City, New York 10003, USA
  • 2Departamento de Física, FCEN, Universidad de Buenos Aires and IFIBA-CONICET Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina

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Phys. Rev. D 112, 064045 – Published 16 September, 2025

DOI: https://doi.org/10.1103/dkqh-8s95

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-Newman-Unti-Tamburino solution, we demonstrate that, near the Kleinian horizons, the geometry exhibits a local infinite-dimensional symmetry generated by supertranslations and super-rotations. 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.

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Phys. Rev. D 112, 064045– Published 16 September, 2025
  • Received 3 June 2025
  • Accepted 31 August 2025
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