A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions

Abstract

We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$. In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots for vacuum polarization in the Schwarzschild-Tangherlini spacetime for odd $d=5,...,11$.

arXiv commentNew references added. Minor edits

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• Semi-Classical Backreaction on Asymptotically Anti-de Sitter Black Holes
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• Unveiling horizons in quantum critical collapse
• Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime
• Computation of $⟨{\Phi }^2⟩$ and quantum fluxes at the polar interior of a spinning black hole
• A mode-sum prescription for the renormalized stress energy tensor on black hole spacetimes
• Quantum vacuum polarization around a Reissner-Nordström black hole in five dimensions
• Classical and Quantum Thermodynamic Systems in Curved Spacetime