  We discuss approximations of the Riemannian geometry near the horizon. If a
D+1 dimensional manifold N has a bifurcate Killing horizon then we approximate
N by a product of the two-dimensional Rindler space and a D-1 dimensional
Riemannian manifold M. We obtain approximate formulas for scalar Green
functions. We study the behaviour of the Green functions near the horizon and
their dimensional reduction. We show that if M is compact then the Green
function near the horizon can be approximated by the Green function of a
two-dimensional quantum field theory. The correction term is exponentially
small away from the horizon. We extend the results to black brane solutions of
supergravity in 10 and 11 dimensions. The near horizon geometry can be
approximated by N=AdS_p x S_q. We discuss Euclidean Green functions on N and
their behaviour near the horizon.
