Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect

Abstract

We investigate quasi-free Hadamard states defined via characteristic initial data on null cones centred at the axis of symmetry in spherically symmetric space-times. We characterize the necessary singular behaviour of null boundary two-point functions such that one can define non-linear observables at this null boundary and give formulas for the calculation of these observables. These results extend earlier characterizations of null boundary states defining Hadamard states in the bulk of the null cone. As an application of our derived formulas, we consider their implications for the semi-classical Einstein equations and calculate the vacuum polarization associated with Hawking radiation near a collapsing body.

34 pages, 6 pages appendix, 3 figures. v2: typographical corrections, reordered bibliography, numbered equations, additional references added, more detail added on certain definitions and derivations in appendix, expanded discussion on Minkowski vacuum state

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Cited by in corpus (5)

• On the initial value problem for semiclassical gravity without and with quantum state collapses
• Kodama-like Vector Fields in Axisymmetric Spacetimes
• The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor
• Gravitational null rays: Covariant Quantization and the Dressing Time
• Semiclassical Gravity Beyond General Relativity: Insights from Torsion