We examine the response of an Unruh-DeWitt particle detector coupled to a massless scalar field on the (3+1)-dimensional Schwarzschild spacetime, in the Boulware, Hartle-Hawking and Unruh states, for static detectors and detectors on circular geodesics, by primarily numerical methods. For the static detector, the response in the HartleHawking state exhibits the known thermality at the local Hawking temperature, and the response in the Unruh state is thermal at the local Hawking temperature in the limit of a large detector energy gap. For the circular-geodesic detector, we find evidence of thermality in the limit of a large energy gap for the Hartle-Hawking and Unruh states, at a temperature that exceeds the Doppler-shifted local Hawing temperature. Detailed quantitative comparisons between the three states are given. The response in the Hartle-Hawking state is compared with the response in the Minkowski vacuum and in the Minkowski thermal state for the corresponding Rindler, drifted Rindler, and circularly accelerated trajectories. The analysis takes place within first-order perturbation theory and relies in an essential way on stationarity. *

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 Bañados-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. * pmxlh1@nottingham.ac.uk

We analyse the response of an arbitrarily-accelerated Unruh-DeWitt detector coupled to a massless scalar field in Minkowski spacetimes of dimensions up to six, working within first-order perturbation theory and assuming a smooth switch-on and switch-off. We express the total transition probability as a manifestly finite and regulator-free integral formula. In the sharp switching limit, the transition probability diverges in dimensions greater than three but the transition rate remains finite up to dimension five. In dimension six, the transition rate remains finite in the sharp switching limit for trajectories of constant scalar proper acceleration, including all stationary trajectories, but it diverges for generic trajectories. The divergence of the transition rate in six dimensions suggests that global embedding spacetime (GEMS) methods for investigating detector response in curved spacetime may have limited validity for generic trajectories when the embedding spacetime has dimension higher than five.Comment: 30 pages. v3: presentational improvement. Published versio

We present novel methods to numerically address the problem of characterizing the response of particle detectors in curved spacetimes. These methods allow for the integration of the Wightman function, at least in principle, in rather general backgrounds. In particular we will use this tool to further understand the nature of conformal massless scalar Hawking radiation from a Schwarzschild black hole in anti-de Sitter space. We do that by studying an Unruh-DeWitt detector at rest above the horizon and in circular geodesic orbit. The method allows us to see that the response rate shows peaks at certain characteristic frequencies, which correspond to the quasinormal modes (QNMs) of the spacetime. It is in principle possible to apply these techniques to more complicated and interesting physical scenarios, e.g. geodesic infall or multiple detector entanglement evolution, or the study of the behaviour of quantum correlations in spacetimes with black hole horizons.

Unruh-DeWitt particle detector models are studied in a variety of time-dependent and timeindependent settings. We work within the framework of first-order perturbation theory and couple the detector to a massless scalar field. The necessity of switching on (off) the detector smoothly is emphasised throughout, and the transition rate is found by taking the sharpswitching limit of the regulator-free and finite response function.The detector is analysed on a variety of spacetimes: d-dimensional Minkowski, the Bañados-Teitelboim-Zanelli (BTZ) black hole, the two-dimensional Minkowski half-plane, two-dimensional Minkowski with a receding mirror, and the two-and four-dimensional Schwarzschild black holes.In d-dimensional Minkowski spacetime, the transition rate is found to be finite up to dimension five. In dimension six, the transition rate diverges unless the detector is on a trajectory of constant proper acceleration, and the implications of this divergence to the global embedding spacetime (GEMS) methods are studied.In three-dimensional curved spacetime, the transition rate for the scalar field in an arbitrary Hadamard state is found to be finite and regulator-free. Then on the Bañados-Teitelboim-Zanelli (BTZ) black hole spacetime, we analyse the detector coupled to the field in the Hartle-Hawking vacua, under both transparent and reflective boundary conditions at infinity. Results are presented for the co-rotating detector, which responds thermally, and for the radially-infalling detector.Finally, detectors on the Schwarzschild black hole are considered. We begin in two dimensions, in an attempt to gain insight by exploiting the conformal triviality, and where we apply a temporal cut-off to regulate the infrared divergence. In four-dimensional Schwarzschild spacetime, we proceed numerically, and the Hartle-Hawking, Boulware and Unruh vacua rates are compared. Results are presented for the case of the static detectors, which respond thermally, and also for the case of co-rotating detectors. i First, I would like to thank my supervisor, Dr Jorma Louko, for always being available to chat, suggesting interesting topics, reading this manuscript and not blushing when I asked silly questions. Sincerely, I doubt that it is possible to find a supervisor with more time for his students or more down to earth. My PhD was funded by the Engineering and Physical Sciences Research Council (EP-SRC) -grant reference number EP/P505038/1 -to whom I am grateful. I thank the Universitas 21 Network for funding in the form of a Universitas 21 Prize Scholarship; this award facilitated a month-long visit to University of British Columbia (UBC). I am also grateful for access to the University of Nottingham High Performance Computing Facility. I thank the Department of Physics and Astronomy at UBC for their hospitality; in particular, I thank Professor Bill Unruh for the interesting discussions and suggestions regarding this work. I also thank Professor Adrian Ottewill, University College Dublin, without whom the four-dimensional Schwarzschi...