Propagator of a scalar field on a stationary slowly varying gravitational background

Abstract

The propagator of a scalar field on a stationary slowly varying in space gravitational background is derived retaining only the second derivatives of the metric. The corresponding one-loop effective action is constructed. The propagator and the effective action turn out to depend nontrivially on the Killing vector defining the vacuum state and the Hamiltonian of a scalar field. The Hawking particle production is described in the quasiclassical approximation and the quasiclassical formula for the Hawking temperature is derived. The behaviour of the Unruh detector on a curved background is considered and the quasiclassical formula for the Unruh acceleration determining the Unruh temperature is derived. The radiation reaction problem on a curved background is discussed in view of the new approximate expression for the propagator. The correction to the mass squared of a scalar particle on a stationary gravitational background is obtained. This correction is analogous to the quantum correction to the particle mass in a strong electromagnetic field. For a vacuum solution to the Einstein equations, it is equal to minus one-fourth of the free fall acceleration squared.

arXiv comment45 pp., 1 fig; some misprints corrected, references and appendix added; exposition improved, app. C added

References in corpus (9)

• The Confrontation between General Relativity and Experiment
• Gravity with a dynamical preferred frame
• Prospects for Large Relativity Violations in Matter-Gravity Couplings
• Effective Action of Vacuum: Semiclassical Approach
• Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher-derivative quantum gravity
• On 4D-Hawing Radiation from Effective Action
• Boundary conditions in the Unruh problem
• One-loop effective potential of the Higgs field on the Schwarzschild background
• Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity

Cited by in corpus (4)

• High-temperature expansion of the one-loop free energy of a scalar field on a curved background
• Non-perturbative corrections to the one-loop free energy induced by a massive scalar field on a stationary slowly varying in space gravitational background
• Quantum gravitational anomaly as a dark matter
• Large mass expansion of the one-loop effective action induced by a scalar field on the two-dimensional Minkowski background with non-trivial $(1+1)$ splitting