4 research outputs found
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