Regular Quantum States on the Cauchy Horizon of a Charged Black Hole

Abstract

We consider the quantum stress-energy tensor of a massless scalar field near the Cauchy horizon interior to the Reissner-Nordström black hole spacetime. We construct the quantum state by considering the two-point function on a negative definite metric obtained by a double analytic continuation from the Lorentzian manifold, complexifying both the $t$ and polar coordinates. We enforce periodicity in the Euclideanized $t$ coordinate with periodicity equal to the reciprocal of the temperature of the Cauchy horizon, a necessary condition for avoiding a conical singularity at the inner horizon. We show by explicit construction that our quantum state satisfies the Hadamard condition on the Cauchy horizon. The expectation value of the quantum stress-energy tensor on the Cauchy horizon is given in closed form.

Corrected an error in the uniform asymptotic analysis. Also significantly changed the development of the asymptotic analysis. New Appendix added

References in corpus (6)

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• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• Analysis of quantum effects inside spherical charged black holes
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• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
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Cited by in corpus (7)

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• Hawking radiation inside a charged black hole
• Hadamard renormalization for a charged scalar field
• Renormalization of $⟨{\varphi }^2⟩$ at the inner horizon of rotating, accreting black holes
• Wave equations in conformally separable, accreting, rotating black holes
• Pancakification and negative Hawking temperatures