Transition rate of the Unruh-DeWitt detector in curved spacetime

TL;DR

This paper derives a regulator-free formula for the transition rate of the Unruh-DeWitt detector in curved spacetime, demonstrating its applicability in various gravitational settings and estimating negligible gravitational effects on atomic decay rates.

Contribution

It introduces a regulator-free integral formula for the detector's transition rate in curved spacetime, extending previous Minkowski space results and applying it to gravitational scenarios.

Findings

Derived a regulator-free transition rate formula

Applied the formula to inertial detectors in Rindler vacuum

Estimated gravitational effects on atomic decay rates to be negligible

Abstract

We examine the Unruh-DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.