Discussion on Event Horizon and Quantum Ergosphere of Evaporating Black Holes in a Tunnelling Framework

In this paper, with the Parikh-Wilczek tunnelling framework the positions of the event horizon of the Vaidya black hole and the Vaidya-Bonner black hole are calculated respectively. We find that the event horizon and the apparent horizon of these two black holes correspond respectively to the two turning points of the Hawking radiation tunnelling barrier. That is, the quantum ergosphere coincides with the tunnelling barrier. Our calculation also implies that the Hawking radiation comes from the apparent horizon.Comment: 8 page

Hawking Radiation of Dirac Particles in an Arbitrarily Accelerating Kinnersley Black Hole

Quantum thermal effect of Dirac particles in an arbitrarily accelerating Kinnersley black hole is investigated by using the method of generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the advanced time and the angles. The Hawking thermal radiation spectrum of Dirac particles contains a new term which represents the interaction between particles with spin and black holes with acceleration. This spin-acceleration coupling effect is absent from the thermal radiation spectrum of scalar particles.Comment: Revtex, 12pt, 16 pages, no figure, to appear in Gen. Rel. Grav. 34 (2002) N0.

A Generalized Representation Formula for Systems of Tensor Wave Equations

In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.Comment: 29 page

Hawking Radiation of Dirac Particles in a Variable-mass Kerr Space-time

Hawking effect of Dirac particles in a variable-mass Kerr space-time is investigated by using a method called as the generalized tortoise coordinate transformation. The location and the temperature of the event horizon of the non-stationary Kerr black hole are derived. It is shown that the temperature and the shape of the event horizon depend not only on the time but also on the angle. However, the Fermi-Dirac spectrum displays a residual term which is absent from that of Bose-Einstein distribution.Comment: 12 pages in 12pt Revtex, no figure, to appear in Gen. Rel. Grav. Vol.33, No.7 (2001

Back reaction, covariant anomaly and effective action

In the presence of back reaction, we first produce the one-loop corrections for the event horizon and Hawking temperature of the Reissner-Nordstr\"om black hole. Then, based on the covariant anomaly cancelation method and the effective action technique, the modified expressions for the fluxes of gauge current and energy momentum tensor, due to the effect of back reaction, are obtained. The results are consistent with the Hawking fluxes of a (1+1)-dimensional blackbody at the temperature with quantum corrections, thus confirming the robustness of the covariant anomaly cancelation method and the effective action technique for black holes with back reaction.Comment: 17 page

The Measure for the Multiverse and the Probability for Inflation

We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single field slow roll inflation to last for $N$ e-folds is suppressed by a factor $\exp(-3N)$, and the probability for the generalized $n$-field slow roll inflation is suppressed by a much larger factor $\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not suffer from this difficulty.Comment: 16 page

On Self-Dual Gravity I

(One typo corrected and one incorrect statement removed. Extra details on conserved quantities and symmetry algebras added).Comment: 17 pages, Latex, DAMTP-R92/4

Geometric Thermodynamics of Schwarzschild-AdS black hole with a Cosmological Constant as State Variable

The thermodynamics of the Schwarzschild-AdS black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Different choices of the metric in the equilibrium states manifold are used in order to reproduce the Hawking-Page phase transition as a divergence of the thermodynamical curvature scalar. We show that the enthalpy and total energy representations of GTD does not reproduce the transition while the entropy rep- resentation gives the expected behavior.Comment: 14 page

Quantum corrections and black hole spectroscopy

In the work \cite{BRM,RBE}, black hole spectroscopy has been successfully reproduced in the tunneling picture. As a result, the derived entropy spectrum of black hole in different gravity (including Einstein's gravity, Einstein-Gauss-Bonnet gravity and Ho\v{r}ava-Lifshitz gravity) are all evenly spaced, sharing the same forms as $S_n=n$, where physical process is only confined in the semiclassical framework. However, the real physical picture should go beyond the semiclassical approximation. In this case, the physical quantities would undergo higher-order quantum corrections, whose effect on different gravity shares in different forms. Motivated by these facts, in this paper we aim to observe how quantum corrections affect black hole spectroscopy in different gravity. The result shows that, in the presence of higher-order quantum corrections, black hole spectroscopy in different gravity still shares the same form as $S_n=n$, further confirming the entropy quantum is universal in the sense that it is not only independent of black hole parameters, but also independent of higher-order quantum corrections. This is a desiring result for the forthcoming quantum gravity theory.Comment: 14 pages, no figure, use JHEP3.cls. to be published in JHE

Running Spectral Index and Formation of Primordial Black Hole in Single Field Inflation Models

A broad range of single field models of inflation are analyzed in light of all relevant recent cosmological data, checking whether they can lead to the formation of long-lived Primordial Black Holes (PBHs). To that end we calculate the spectral index of the power spectrum of primordial perturbations as well as its first and second derivatives. PBH formation is possible only if the spectral index increases significantly at small scales, i.e. large wave number $k$. Since current data indicate that the first derivative $\alpha_S$ of the spectral index $n_S(k_0)$ is negative at the pivot scale $k_0$, PBH formation is only possible in the presence of a sizable and positive second derivative ("running of the running") $\beta_S$. Among the three small-field and five large-field models we analyze, only one small-field model, the "running mass" model, allows PBH formation, for a narrow range of parameters. We also note that none of the models we analyze can accord for a large and negative value of $\alpha_S$, which is weakly preferred by current data.Comment: 26 pages, 5 figures, Refs. added, Minor textual change; version to appear in JCA