### Abstract

The complete form of 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 stationary spacetime. In particular, we confirm that 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 nonstatic 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. The natural simplest Lagrangian for the "Killing vector field" is given.

Original language | English |
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Article number | 084036 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 87 |

Issue number | 8 |

DOIs | |

Publication status | Published - 12 Apr 2013 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*87*(8), [084036]. https://doi.org/10.1103/PhysRevD.87.084036