Hawking Radiation as Tunneling: the D-dimensional rotating case

The tunneling method for the Hawking radiation is revisited and applied to the $D$ dimensional rotating case. Emphasis is given to covariance of results. Certain ambiguities afflicting the procedure are resolved.Comment: Talk delivered at the Seventh International Workshop Quantum Field Theory under the influence of External Conditions, QFEXT'05, september 05,Barcelona, Spain. To appear in Journal of Phys.

On the semiclassical treatment of Hawking radiation

In the context of the semiclassical treatment of Hawking radiation we prove the universality of the reduced canonical momentum for the system of a massive shell self gravitating in a spherical gravitational field within the Painlev\'e family of gauges. We show that one can construct modes which are regular on the horizon both by considering as hamiltonian the exterior boundary term and by using as hamiltonian the interior boundary term. The late time expansion is given in both approaches and their time Fourier expansion computed to reproduce the self reaction correction to the Hawking spectrum.Comment: 18 pages, LaTeX, Corrected typo

Problems with Tunneling of Thin Shells from Black Holes

It is shown that $exp(-2 Im(\int p dr))$ is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However it is shown that this gives half the correct temperature for black holes.Comment: 25 pages, 3 figures; v4: Made changes for publicatio

Tunnelling through black rings

Hawking radiation of black ring solutions to 5-dimensional Einstein-Maxwell-dilaton gravity theory is analyzed by use of the Parikh-Wilczek tunnelling method. To get the correct tunnelling amplitude and emission rate, we adopted and developed the Angheben-Nadalini-Vanzo-Zerbini covariant approach to cover the effects of rotation and electronic discharge all at once, and the effect of back reaction is also taken into account. This constitute a unified approach to the tunnelling problem. Provided the first law of thermodynamics for black rings holds, the emission rate is proportional to the exponential of the change of Bekenstein-Hawking entropy. Explicit calculation for black ring temperatures agree exactly with the results obtained via the classical surface gravity method and the quasilocal formalism.Comment: 10 pages, V2: various modifications throughout the text, plus a lot of newly added reference

Hawking Radiation as Tunneling for Extremal and Rotating Black Holes

The issue concerning semi-classical methods recently developed in deriving the conditions for Hawking radiation as tunneling, is revisited and applied also to rotating black hole solutions as well as to the extremal cases. It is noticed how the tunneling method fixes the temperature of extremal black hole to be zero, unlike the Euclidean regularity method that allows an arbitrary compactification period. A comparison with other approaches is presented.Comment: 17 pages, Latex document, typos corrected, four more references, improved discussion in section

Hamilton-Jacobi Tunneling Method for Dynamical Horizons in Different Coordinate Gauges

Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions on the sign of the energy.Comment: Standard Latex document, typos corrected, refined discussion of tunneling picture, subsection 5.1 remove

Fermions Tunnelling from Black Holes

We investigate the tunnelling of spin 1/2 particles through event horizons. We first apply the tunnelling method to Rindler spacetime and obtain the Unruh temperature. We then apply fermion tunnelling to a general non-rotating black hole metric and show that the Hawking temperature is recovered.Comment: 22 pages, v2: added references, v3: fixed minor typos, v4: added a new section applying fermion tunnelling method to Kruskal-Szekers coordinates, fixed minor typo, and added references, v5: modified introduction and conclusion, fixed typo

Tunnelling Methods and Hawking's radiation: achievements and prospects

The aim of this work is to review the tunnelling method as an alternative description of the quantum radiation from black holes and cosmological horizons. The method is first formulated and discussed for the case of stationary black holes, then a foundation is provided in terms of analytic continuation throughout complex space-time. The two principal implementations of the tunnelling approach, which are the null geodesic method and the Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The Hamilton-Jacobi method is then extended to cover spherically symmetric dynamical black holes, cosmological horizons and naked singularities. Prospects and achievements are discussed in the conclusions.Comment: Topical Review commissioned and accepted for publication by "Classical and Quantum Gravity". 101 pages; 6 figure

Discontinuities in Scalar Perturbations of Topological Black Holes

We study the perturbative behaviour of topological black holes. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations. In the case of small black holes we find discontinuities of the quasi-normal modes spectrum at the critical temperature and we argue that this is evidence of a second-order phase transition.Comment: 23 pages, 17 figures, published versio

Unruh--DeWitt detectors in spherically symmetric dynamical space-times

In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein--de Sitter universe (that is a more realistic situation in the frame of $\Lambda$CDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.Comment: 19 pages, to appear on IJTP. arXiv admin note: substantial text overlap with arXiv:1101.525