The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

Christian Gérard (1) , Dietrich Häfner (2) , Michał Wrochna (2)

1 Département de Mathématiques [ORSAY]
2 IF - Institut Fourier

We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically thermal at Hawking temperature on the past event horizon. Furthermore, we demonstrate that in the union of the exterior and interior regions, the Unruh state is pure and Hadamard. The main ingredients are the Häfner-Nicolas scattering theory, new microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions.

Domaines: Physique mathématique [math-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]; Equations aux dérivées partielles [math.AP]; Physique des Hautes Energies - Théorie [hep-th]

Christian Gérard, Dietrich Häfner, Michał Wrochna. The Unruh state for massless fermions on Kerr spacetime and its Hadamard property. 2020. ⟨hal-02927644⟩