Stress-energy tensor of the quantized massive fields in Schwarzschild-Tangherlini spacetimes. The back reaction

Abstract

We construct and study the approximate stress-energy tensor of the quantized massive scalar field in higher dimensional Schwarzschild-Tangherlini spacetimes. The stress-energy tensor is calculated within the framework of the Schwinger-DeWitt approach. It is shown that in $N$-dimensional spacetime the main approximation can be obtained from the effective action constructed form the coincidence limit of the Hadamard-DeWitt coefficient $a_k,$ where $k-1$ is the integer part of $N/2$. The back reaction of the quantized field upon the black hole spacetime is analyzed and the quantum-corrected Komar mass and the Hawking temperature is calculated. It is shown that for the minimal and conformal coupling the increase of the Komar mass of the quantum corrected black hole leads to the decrease of its Hawking temperature. This is not generally true for more exotic values of the coupling parameter. The general formula describing the vacuum polarization, $⟨{\varphi }^2⟩,$ is constructed and briefly examined.

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• The Hawking effect and the bounds on greybody factor for higher dimensional Schwarzschild black holes
• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
• A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions
• Stress-energy tensor of quantized massive fields in static wormhole spacetimes
• Inside the Schwarzschild-Tangherlini black holes
• Vacuum polarization of the quantized massive scalar field in the global monopole spacetime II: the renormalized quantum stress energy tensor
• Stress-energy of the quantized fields in the spacetime of the Damour-Solodukhin wormhole
• Black Hole Quantum Vacuum Polarization in Higher Dimensions