Exploring quantum fields in rotating black holes

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, Ann. Henri Poincare 24(7), 2401–2442 (2023)] 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 and C. Klein, Lett. Math. Phys. 114(5), 119 (2024)] 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 et al., Phys. Rev. Lett. 132(12), 121501 (2024)], and describe a universality result for these effects [P. Hintz and C. Klein, Classical Quantum Gravity 41(7), 075006 (2024)].