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).
Christiane Klein (Sun,) studied this question.