Construction of the Unruh State for a Real Scalar Field on the Kerr-de Sitter Spacetime

Abstract

The study of physical effects of quatum fields in black hole spacetimes, which is related to questions such as the validity of the strong cosmic censorship conjecture, requires a Hadamard state describing the physical situation. Here, we consider the theory of a free scalar field on a Kerr-de Sitter spacetime, focussing on spacetimes with sufficiently small angular momentum of the black hole and sufficiently small cosmological constant. We demonstrate that an extension of the Unruh state, which describes the expected late-time behaviour in spherically symmetric gravitational collapse, can be rigorously constructed for the free scalar field on such Kerr-de Sitter spacetimes. In addition, we show that this extension of the Unruh state is a Hadamard state in the black hole exterior and in the black hole interior up to the inner horizon. This provides a physically motivated Hadamard state for the study of free scalar fields in rotating black hole spacetimes.

42 pages, 4 figures, 2 appendices, version as accepted for publication in Ann. Henri Poincaré

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Cited by in corpus (7)

• Generalized Black Hole Entropy is von Neumann Entropy
• Backreaction from quantum fluxes at the Kerr inner horizon
• Infinite quantum twisting at the Cauchy horizon of rotating black holes
• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Hadamard property of the Unruh state for massless fermions on Kerr spacetime : the large $a$ case
• Computation of $⟨{\Phi }^2⟩$ and quantum fluxes at the polar interior of a spinning black hole
• Exploring quantum fields in rotating black holes