A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions

Abstract

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function $f(r)$. As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even $d=4,...,10$. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.

arXiv admin note: text overlap with arXiv:1609.08166

References in corpus (5)

• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes
• Stress-energy tensor of the quantized massive fields in Schwarzschild-Tangherlini spacetimes. The back reaction

Cited by in corpus (2)

• Stress-energy tensor of quantized massive fields in static wormhole spacetimes
• Classical and Quantum Thermodynamic Systems in Curved Spacetime