Time and temperature in semi-classical gravity

Abstract

It is shown how in the functional integral approach, time arises as a natural parametrization for the way matter adiabatically follows gravitational configurations where the latter are treated in the semi-classical approximation. In the presence of horizons this time becomes complex and if the motion is periodic “behind the horizon” such functional integrals become partition functions. So the functional integral approach naturally associates the very concept of time and horizon thermal radiation.