Exploring quantum fields in rotating black holes

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 Poincaré 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. Häfner, 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. Klein, Class.Quant.Grav. 41 (2024) 7, 075006].

18 pages, 2 figures, invited contribution to the Special Topic on "XXI International Congress on Mathematical Physics 2024" in Journal of Mathematical Physics