Abstract
The decay of extremal charged black holes has been a useful guidance to derive consistency conditions in quantum gravity. In de Sitter space it has been argued that requiring (extremal) charged Nariai black holes to decay without forming a big crunch singularity yields the Festina Lente (FL) bound: particles with mass ms and charge q should satisfy \( {m}_s^2\gg {M}_p Hq \), where Mp is the Planck mass and H the Hubble parameter. Using a tunneling approach we show that the decay probability of charged black holes in de Sitter space in the s-wave sector is P ∼ exp(∆Sb), where ∆Sb is the change in the black hole entropy. We find that the FL bound corresponds to ∆Sb ≤ – 1 in the Nariai and probe limit. However, taking into account backreaction we identify unsuppressed decay channels, which might be subdominant, that violate this bound but nonetheless do not result in a big crunch for every observer.
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Acknowledgments
We would like to thank Miguel Montero, Thomas Van Riet, and Gerben Venken for useful discussions about the interpretation of the FL bound. LA likes to thank the hospitality of the UW-Madison High-Energy Theory group, where part of this work was completed, and Yoshihiko Abe, Puxin Lin and Gary Shiu for useful discussions on related topics. This work benefited from discussions arising at the DAMTP workshop “Quantum de Sitter Universe”, funded by the Gravity Theory Trust and the Centre for Theoretical Cosmology. This work is part of the Delta ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). LA is supported by the Heising-Simons Foundation under the “Observational Signatures of Quantum Gravity” collaboration grant 2021-2818. MRV is supported by SNF Postdoc Mobility grant P500PT-206877 “Semi-classical thermodynamics of black holes and the information paradox”.
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Aalsma, L., van der Schaar, J.P. & Visser, M.R. Extremal black hole decay in de Sitter space. J. High Energ. Phys. 2024, 259 (2024). https://doi.org/10.1007/JHEP07(2024)259
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DOI: https://doi.org/10.1007/JHEP07(2024)259