1301.5103 (I. S. Kalinichenko et al.)

High-temperature expansion of the one-loop free energy of a scalar field
on a curved background    [PDF]

I. S. Kalinichenko, P. O. Kazinski

The high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the high-temperature expansion in a three-dimensional space without boundaries are obtained. These formulas generalize the known one for the static spacetime. In particular, for a massless conformal scalar field, the leading correction to the Planck law proportional to the temperature squared turns out to be nonzero due to the non-static nature of the metric. The explicit expression for the so-called energy-time anomaly is found. The interrelation between this anomaly and the conformal (trace) anomaly is established.

View original: http://arxiv.org/abs/1301.5103