$<{\varphi }^2>$ in the Spacetime of a Cylindrical Black Hole

Abstract

The renormalised value of $<{\varphi }^2>$ is calculated for a massless, conformally coupled scalar field in the Hartle-Hawking vacuum state. This calculation is a first step towards the calculation of the gravitational back reaction of the field in a black cosmic string spacetime which is asymptotically anti-DeSitter and possesses a non constant dilaton field. It is found that the field is divergence free throughout the spacetime and attains its maximum value near the horizon.

16 pages with AMS fonts. Update includes corrections as well as figure

References in corpus (5)

• Black holes with unusual topology
• Semiclassical effects in black hole interiors
• Gravitational collapse to toroidal, cylindrical and planar black holes
• Vacuum polarization around a three-dimensional black hole
• Quantum Fields near Black Holes

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• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time
• Quantization of massive scalar fields over static black string backgrounds
• Vacuum polarization of massive spinor fields in static black-string backgrounds
• Vacuum polarization on the brane
• Vacuum polarization on topological black holes with Robin boundary conditions
• Vacuum currents in partially compactified Rindler spacetime with an application to cylindrical black holes
• Vacuum polarization on topological black holes
• Quantum stress tensor for massive vector field in the space-time of a cylindrical black hole