How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.Comment: 30 pages, 1 figure. v3: Added references and minor clarification

Observer Dependent Horizon Temperatures: a Coordinate-Free Formulation of Hawking Radiation as Tunneling

We reformulate the Hamilton-Jacobi tunneling method for calculating Hawking radiation in static, spherically-symmetric spacetimes by explicitly incorporating a preferred family of frames. These frames correspond to a family of observers tied to a locally static timelike Killing vector of the spacetime. This formulation separates the role of the coordinates from the choice of vacuum and thus provides a coordinate-independent formulation of the tunneling method. In addition, it clarifies the nature of certain constants and their relation to these preferred observers in the calculation of horizon temperatures. We first use this formalism to obtain the expected temperature for a static observer at finite radius in the Schwarzschild spacetime. We then apply this formalism to the Schwarzschild-de Sitter spacetime, where there is no static observer with 4-velocity equal to the static timelike Killing vector. It is shown that a preferred static observer, one whose trajectory is geodesic, measures the lowest temperature from each horizon. Furthermore, this observer measures horizon temperatures corresponding to the well-known Bousso-Hawking normalization.Comment: 11 pages, 1 2-part figure, references added, appendix added, discussion streamline

Back reaction, emission spectrum and entropy spectroscopy

Recently, an interesting work, which reformulates the tunneling framework to directly produce the Hawking emission spectrum and entropy spectroscopy in the tunneling picture, has been received a broad attention. However, during the emission process, most related observations have not incorporated the effects of back reaction on the background spacetime, whose derivations are therefore not the desiring results for the real physical process. With this point as a central motivation, in this paper we suitably adapt the \emph{reformulated} tunneling framework so that it can well accommodate the effects of back reaction to produce the Hawking emission spectrum and entropy spectroscopy. Consequently, we interestingly find that, when back reaction is considered, the Parikh-Wilczek's outstanding observations that, an isolated radiating black hole has an unitary-evolving emission spectrum that is \emph{not} precisely thermal, but is related to the change of the Bekenstein-Hawking entropy, can also be reproduced in the reformulated tunneling framework, meanwhile the entropy spectrum has the same form as that without inclusion of back reaction, which demonstrates the entropy quantum is \emph{independent} of the effects of back reaction. As our final analysis, we concentrate on the issues of the black hole information, but \emph{unfortunately} find that, even including the effects of back reaction and higher-order quantum corrections, such tunneling formalism can still not provide a mechanism for preserving the black hole information.Comment: 16 pages, no figure, use JHEP3.cls. to be published in JHE