Static, stationary and inertial Unruh-DeWitt detectors on the BTZ black hole

Abstract

We examine an Unruh-DeWitt particle detector coupled to a scalar field in three-dimensional curved spacetime. We first obtain a regulator-free expression for the transition probability in an arbitrary Hadamard state, working within first-order perturbation theory and assuming smooth switching, and we show that both the transition probability and the instantaneous transition rate remain well defined in the sharp switching limit. We then analyse a detector coupled to a massless conformally coupled field in the Hartle-Hawking vacua on the Banados-Teitelboim-Zanelli black hole, under both transparent and reflective boundary conditions at the infinity. A selection of stationary and freely-falling detector trajectories are examined, including the co-rotating trajectories, for which the response is shown to be thermal. Analytic results in a number of asymptotic regimes, including those of large and small mass, are complemented by numerical results in the interpolating regimes. The boundary condition at infinity is seen to have a significant effect on the transition rate.

31 pages, 28 figures. v3: minor corrections and clarifications

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• The Unruh effect and its applications
• How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile
• Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?
• Accelerating Branes and Brane Temperature

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• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour
• Unruh-DeWitt detector on the BTZ black hole
• Hawking and Unruh radiation perception by different observers: applications of the effective temperature function (in Spanish)