On the Hartle-Hawking-Israel states for spacetimes with static bifurcate Killing horizons
Christian G\'erard (LM-Orsay)
TL;DR
This paper provides a simplified proof that the Hartle-Hawking-Israel state for a quantum Klein-Gordon field on certain spacetimes has the Hadamard property, using advanced mathematical tools.
Contribution
It offers a new, concise proof of the Hadamard property for the Hartle-Hawking-Israel state employing Calderón projectors and pseudodifferential calculus.
Findings
Confirmed the Hadamard property of the state using new methods
Simplified the mathematical proof process
Enhanced understanding of quantum states on spacetimes with horizons
Abstract
We revisit the construction by Sanders [S1] of the Hartle-Hawking-Israel state for a free quantum Klein-Gordon field on a spacetime with a static, bifurcate Killing horizon and a wedge reflection. Using the notion of the Calder{\'o}n projector for elliptic boundary value problems and pseudodifferential calculus on manifolds, we give a short proof of its Hadamard property.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Advanced Mathematical Physics Problems · Noncommutative and Quantum Gravity Theories