Quantum gravitational corrections to the stress-energy tensor around the rotating BTZ black hole

Abstract

Modes emerging out of a collapsing black hole are red-shifted to such an extent that Hawking radiation at future null infinity consists of modes that have energies beyond the Planck scale at past null infinity. This indicates that physics at the Planck scale may modify the spectrum of Hawking radiation and the associated stress-energy tensor of the quantum field. Recently, it has been shown that, the T-duality symmetry of string fluctuations along compact extra dimensions leads to a modification of the standard propagator of point particles in quantum field theory. At low energies (when compared to the string scale), the modified propagator is found to behave as though the spacetime possesses a minimal length, say, $\lp$, which we shall assume to be of the order of the Planck length. We utilize the duality approach to evaluate the modified propagator around the rotating Banados-Teitelboim-Zanelli black hole and show that the propagator is finite in the coincident limit. We compute the stress-energy tensor associated with the modified Green's function and illustrate graphically that the quantum gravitational corrections turn out to be negligibly small. We conclude by briefly commenting on the results we have obtained.

v1. 7 pages, 2 figures; v2. 11 pages, 4 figures, discussion extended to the case of the rotating BTZ black hole, figures improved

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• Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions