Green functions and Euclidean fields near the bifurcate Killing horizon
نویسنده
چکیده
We approximate a Euclidean version of a D + 1 dimensional manifold with a bifurcate Killing horizon by a product of the two dimensional Rindler space R2 and a D − 1 dimensional Riemannian 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. 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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