Conformal Scalar Propagation and Hawking Radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by S. Hawking on the relation between quantum propagation and observation of particles produced by a black hole.Comment: 18 pages, 2 figures, one footnote removed, motto added. Due to appear in General Relativity and Gravitatio

Effective temperature for black holes

The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes are natural candidates for an interpretation in terms of quantum levels. The spectrum of black hole's quasinormal modes can be re-analysed by introducing a black hole's effective temperature which takes into account the fact that, as shown by Parikh and Wilczek, the radiation spectrum cannot be strictly thermal. This issue changes in a fundamental way the physical understanding of such a spectrum and enables a re-examination of various results in the literature which realizes important modifies on quantum physics of black holes. In particular, the formula of the horizon's area quantization and the number of quanta of area result modified becoming functions of the quantum "overtone" number n. Consequently, the famous formula of Bekenstein-Hawking entropy, its sub-leading corrections and the number of microstates are also modified. Black hole's entropy results a function of the quantum overtone number too. We emphasize that this is the first time that black hole's entropy is directly connected with a quantum number. Previous results in the literature are re-obtained in the limit n \to \infty.Comment: 10 pages,accepted for publication in Journal of High Energy Physics. Comments are welcom

The hidden horizon and black hole unitarity

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic "exclusive backgrounds" to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such "inclusive background" presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes 3 and 5

On Symmetries of Extremal Black Holes with One and Two Centers

After a brief introduction to the Attractor Mechanism, we review the appearance of groups of type E7 as generalized electric-magnetic duality symmetries in locally supersymmetric theories of gravity, with particular emphasis on the symplectic structure of fluxes in the background of extremal black hole solutions, with one or two centers. In the latter case, the role of an "horizontal" symmetry SL(2,R) is elucidated by presenting a set of two-centered relations governing the structure of two-centered invariant polynomials.Comment: 1+13 pages, 2 Tables. Based on Lectures given by SF and AM at the School "Black Objects in Supergravity" (BOSS 2011), INFN - LNF, Rome, Italy, May 9-13 201

Entanglement generation outside a Schwarzschild black hole and the Hawking effect

We examine the Hawking effect by studying the asymptotic entanglement of two mutually independent two-level atoms placed at a fixed radial distance outside a Schwarzschild black hole in the framework of open quantum systems. We treat the two-atom system as an open quantum system in a bath of fluctuating quantized massless scalar fields in vacuum and calculate the concurrence, a measurement of entanglement, of the equilibrium state of the system at large times, for the Unruh, Hartle-Hawking and Boulware vacua respectively. We find, for all three vacuum cases, that the atoms turn out to be entangled even if they are initially in a separable state as long as the system is not placed right at the even horizon. Remarkably, only in the Unruh vacuum, will the asymptotic entanglement be affected by the backscattering of the thermal radiation off the space-time curvature. The effect of the back scatterings on the asymptotic entanglement cancels in the Hartle-Hawking vacuum case.Comment: 15 pages, no figures, Revte

Generalized Painleve-Gullstrand descriptions of Kerr-Newman black holes

Generalized Painleve-Gullstrand metrics are explicitly constructed for the Kerr-Newman family of charged rotating black holes. These descriptions are free of all coordinate singularities; moreover, unlike the Doran and other proposed metrics, an extra tunable function is introduced to ensure all variables in the metrics remain real for all values of the mass M, charge Q, angular momentum aM, and cosmological constant \Lambda > - 3/(a^2). To describe fermions in Kerr-Newman spacetimes, the stronger requirement of non-singular vierbein one-forms at the horizon(s) is imposed and coordinate singularities are eliminated by local Lorentz boosts. Other known vierbein fields of Kerr-Newman black holes are analysed and discussed; and it is revealed that some of these descriptions are actually not related by physical Lorentz transformations to the original Kerr-Newman expression in Boyer-Lindquist coordinates - which is the reason complex components appear (for certain ranges of the radial coordinate) in these metrics. As an application of our constructions the correct effective Hawking temperature for Kerr black holes is derived with the method of Parikh and Wilczek.Comment: 5 pages; extended to include application to derivation of Hawking radiation for Kerr black holes with Parikh-Wilczek metho

Holographic phase transition from dyons in an AdS black hole background

We construct a dyon solution for a Yang-Mills-Higgs theory in a 4 dimensional Schwarzschild-anti-de Sitter black hole background with temperature T. We then apply the AdS/CFT correspondence to describe the strong coupling regime of a 2+1 quantum field theory which undergoes a phase transition exhibiting the condensation of a composite charge operator below a critical temperature $T_c$.Comment: 19 pages, 7 figures. Minor corrections, references added. Version published in JHEP

Topological Static Spherically Symmetric vacuum Solutions in F(R,G)\mathcal F(R,G) Gravity

The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $\mathcal F (R,G)$-modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $\mathcal F (R,G)=R+\sqrt{G}$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived.Comment: 12 pages, minor corrections, published versio

The Stokes Phenomenon and Quantum Tunneling for de Sitter Radiation in Nonstationary Coordinates

We study quantum tunneling for the de Sitter radiation in the planar coordinates and global coordinates, which are nonstationary coordinates and describe the expanding geometry. Using the phase-integral approximation for the Hamilton-Jacobi action in the complex plane of time, we obtain the particle-production rate in both coordinates and derive the additional sinusoidal factor depending on the dimensionality of spacetime and the quantum number for spherical harmonics in the global coordinates. This approach resolves the factor of two problem in the tunneling method.Comment: LaTex 10 pages, no figur

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