Extended Green-Liouville asymptotics and vacuum polarization for lukewarm black holes

Abstract

We consider a quantum field on a lukewarm black hole spacetime. We introduce a new uniform approximation to the radial equation, constructed using an extension of Green-Liouville asymptotics. We then use this new approximation to construct the renormalized vacuum polarization in the Hartle-Hawking vacuum. Previous calculations of the vacuum polarization rely on the WKB approximation to the solutions of the radial equation, however the nonuniformity of the WKB approximations obscures the results of these calculations near both horizons. The use of our new approximation eliminates these obscurities, enabling us to obtain explicitly finite and easily calculable values of the vacuum polarization on the two horizons.

19 pages, 5 figures, RevTeX; Change in terminology due to referees comments, typos corrected. Published in Phys. Rev. D

References in corpus (2)

• Vacuum polarization for lukewarm black holes
• Pade Approximants of the Green Function in Spherically Symmetric Spacetimes

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• Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time
• Vacuum polarization on the brane
• Vacuum polarization on topological black holes with Robin boundary conditions
• Semiclassical lukewarm black holes
• Regular Quantum States on the Cauchy Horizon of a Charged Black Hole
• Lukewarm black holes in quadratic gravity
• Vacuum polarization on topological black holes
• Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime