Exploring quantum fields in rotating black holes
Christiane K.M. Klein
TL;DR
This paper extends the mathematical understanding of quantum fields in rotating black holes, specifically Kerr-de Sitter spacetime, by proving the Hadamard property of the Unruh state for a wider range of black hole parameters and discussing its implications for quantum effects near the inner horizon.
Contribution
It generalizes the proof of the Hadamard property of the Unruh state to all subextreme Kerr-de Sitter black holes, extending previous results and applying geometric analysis of the trapped set.
Findings
Proved Hadamard property for all subextreme Kerr-de Sitter black holes.
Extended geometric analysis of the trapped set to Kerr-de Sitter.
Discussed applications in numerical studies of quantum effects at the inner horizon.
Abstract
In this paper, we discuss the Unruh state for a free scalar quantum field on Kerr-de Sitter under the assumption of mode stability. We summarise the proof of its Hadamard property that was previously given in [C.Klein, Annales Henri Poincar\'e 24 (2023) 7, 2401-2442] for sufficiently small black-hole rotation and cosmological constant, and show how it can be generalised to any subextreme black-hole angular momentum in the same range of the cosmological constant. This is done by extending a geometric analysis of the trapped set of the Kerr spacetime [D. H\"afner, C. Klein, Lett.Math.Phys. 114 (2024) 5, 119] to Kerr-de Sitter. Moreover, we discuss the application of this state in the numerical study of quantum effects at the inner horizon [C. Klein, M. Soltani, M. Casals, S. Hollands, Phys.Rev.Lett. 132 (2024) 12, 121501], and describe a universality result for these effects [P. Hintz, C.…
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