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arXiv · 0708.1742

Green functions and Euclidean fields near the bifurcate Killing horizon

Z. Haba
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Abstract

We approximate a Euclidean version of a D+1 dimensional manifold with a bifurcate Killing horizon by a product of a two-dimensional Rindler space and a D-1 dimensional manifold M. We obtain approximate formulas for the Green functions. We study the behaviour of Green functions near the horizon and their dimensional reduction. We show that if M is compact then the massless minimally coupled quantum field contains a zero mode which is a conformal invariant free field on R^2. Then, the Green function near the horizon can be approximated by the Green function of the two-dimensional quantum field theory. The correction term is exponentially small away from the horizon. If the volume of a geodesic ball is growing to infinity with its radius then the Green function cannot be approximated by a two-dimensional one.

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Z. Haba. 2007-08-13. Green functions and Euclidean fields near the bifurcate Killing horizon. https://arxiv.org/abs/0708.1742

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