The Unruh state for Dirac fields on Kerr spacetime
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Abstract: A long-standing open problem at the intersection of QFT and General Relativity consists in determining the final quantum state arising from the collapse into a black hole and to describe its thermodynamical properties. As a simpler model, we consider massless Dirac fields on slowly rotating Kerr spacetimes. We show that the requirement of smooth extendibility across the future event horizon selects a state which is thermal at Hawking temperature on the past event horizon. This gives the first rigorous construction of the Unruh state on rotating black hole spacetimes. The main ingredients are the scattering theory developed by Häfner–Nicolas, microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions. (joint work with Christian Gérard and Dietrich Häfner)