How many black holes fit on the head of a pin?

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations. Fourth Award in the 2007 Essay Competition of the Gravity Research Foundation.     

“Charged” particle’s tunneling from rotating black holes

The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from rotating black hole can be treated as “charged” particle’s tunneling process in its effectively two dimensional metric. Using this viewpoint and considering the corresponding “gauge charge” conservation, we calculate the non-thermal tunneling rate of Kerr black hole and Myers–Perry black hole, and results are consistent with Parikh–Wilczek’s original result for spherically symmetric black holes. Especially for Myers–Perry black hole which has multi-rotation parameters, our calculation fills in the gap existing in the literature applying Parikh–Wilczek’s tunneling method to various types black holes. Our derivation further illuminates the essential role of effective gauge symmetry in Hawking radiation from rotating black holes.     

Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner–Nordström black hole, the Kerr black hole, and the Kerr–Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.     

Entropy Conservation of Linear Dilaton Black Holes in Quantum Corrected Hawking Radiation

It has been shown recently that information is lost in the Hawking radiation of the linear dilaton black holes in various theories when applying the tunneling formalism of Parikh and Wilczek without considering quantum gravity effects. In this paper, we recalculate the emission probability by taking into account the log-area correction to the Bekenstein-Hawking entropy and the statistical correlation between quanta emitted. The crucial role of the quantum gravity effects on the information leakage and black hole remnant is highlighted. The entropy conservation of the linear dilaton black holes is discussed in detail. We also model the remnant as an extreme linear dilaton black hole with a pointlike horizon in order to show that such a remnant cannot radiate and its temperature becomes zero. In summary, we show that the information can also leak out of the linear dilaton black holes together with preserving unitarity in quantum mechanics.     

Extremal black holes in the Hořava–Lifshitz gravity

We study the near-horizon geometry of extremal black holes in the z=3 Ho?ava–Lifshitz gravity with a flow parameter λ. For λ>1/2, near-horizon geometry of extremal black holes are AdS ₂×S ² with different radii, depending on the (modified) Ho?ava–Lifshitz gravity. For 1/3≤λ≤1/2, the radius v ₂ of S ² is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein–Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein–Hawking entropy of extremal black holes.     

Lectures on attractors and black holes

A basic survey on some aspects of four‐dimensional black holes (BHs) is given in these lectures. It covers thermodynamical properties as well as the Attractor Mechanism for extremal BHs in an environment of scalar field background. Some relevant formulæ for the critical points of the BH “effective potential” are discussed, and the simplest example uncovering the attractor behavior, the Maxwell‐Einstein‐dilaton supergravity, is analyzed in detail. Observations on similarities between BH entropy (as given by the Bekenstein‐Hawking entropy‐area formula) and multipartite entanglement of qubits in quantum information theory are reported, as well. Finally, among the latest developments, the moduli space of attractor points for 𝒩 ≥ 2 supergravities is also considered. Based on lectures given by S. Ferrara at the International School of Subnuclear Physics, 45th Course: Search for the “Totally Unexpected” in the LHC era, Erice, Italy, 29 August – 7 September 2007 (Directors: G. 't Hooft – A. Zichichi), and at the III Avogadro Meeting on Theoretical Physics, Alessandria, Italy, 19 – 21 December 2007.     

Immirzi parameter and quasinormal modes in four and higher spacetime dimensions

There is a one-parameter quantization ambiguity in loop quantum gravity, which is called the Immirzi parameter. In this paper, we fix this free parameter by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. As a consequence, our result is consistent with the Bekenstein–Hawking entropy of a black hole. Moreover, we also give a possible quantum gravity explanation of the universal ln 3 behavior of the quasinormal mode spectrum.     

Hamiltonian evolution and quantization for extremal black holes

We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary conditions appropriate for extremal black holes only. The Hamiltonian contains no surface term at the internal infinity, for reasons related to the vanishing of the extremal hole surface gravity, and quantization yields a vanishing black hole entropy. Second, we give a Hamiltonian quantization that incorporates extremal black holes as a limiting case of nonextremal ones, and examine the classical limit in terms of wave packets. The spreading of the packets, even the ones centered about extremal black holes, is consistent with continuity of the entropy in the extremal limit, and thus with the Bekenstein-Hawking entropy even for the extremal holes. The discussion takes place throughout within Lorentz-signature spacetimes.     

Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a p-dimensional torus, for D = (10 − p) = 4,…,9. We study in particular a one-parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.     

LETTER: Entropy Using Path Integrals for Quantum Black Hole Models

Canonical quantum gravity has been used in the search for eigenvalue equations that could describe black holes. In this paper we choose one of the simplest of these quantum equations to show how the usual Feynman's path integral approach can be applied to get the corresponding statistical properties. We get a logarithmic correction to the Bekenstein–Hawking entropy as already obtained by other authors by other means.     

Quantum corrections to the entropy of charged rotating black holes

Hawking radiation from a black hole can be viewed as quantum tunneling of particles through the event horizon. Using this approach we provide a general framework for studying corrections to the entropy of black holes beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics, we study charged rotating black holes and explicitly work out the corrections to entropy and horizon area for the Kerr–Newman and charged rotating BTZ black holes. It is shown that the results for other geometries like the Schwarzschild, Reissner-Nordström and anti-de Sitter–Schwarzschild spacetimes follow easily.     

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data—the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2{{\mathcal N}=2} supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner–Nordstrom black holes in ordinary Einstein–Maxwell theory.     

LETTER: The Life and Times of Extremal Black Holes

Charged extremal black holes cannot fully evaporate through the Hawking effect and are thus long lived. Over their lifetimes, these black holes take part in a variety of astrophysical processes, including many that lead to their eventual destruction. This paper explores the various events that shape the life of extremal black holes and calculates the corresponding time scales.     

Charged fermions tunneling from regular black holes

We study Hawking radiation of charged fermions as a tunneling process from charged regular black holes, i.e., the Bardeen and ABGB black holes. For this purpose, we apply the semiclassical WKB approximation to the general covariant Dirac equation for charged particles and evaluate the tunneling probabilities. We recover the Hawking temperature corresponding to these charged regular black holes. Further, we consider the back-reaction effects of the emitted spin particles from black holes and calculate their corresponding quantum corrections to the radiation spectrum. We find that this radiation spectrum is not purely thermal due to the energy and charge conservation but has some corrections. In the absence of charge, e = 0, our results are consistent with those already present in the literature.     

The uncertainty principle and Bekenstein–Hawking entropy corrections

There is much attention on the corrections to Bekenstein–Hawking entropy in area with a model-dependent coefficient. The corrections are generally composed of two parts: quantum corrections and thermal corrections. The generalized uncertainty principle (GUP), which will reduce to the conventional Heisenberg relation in situations of weak gravity, is one of the candidates to be utilized to obtain the quantum corrections to the Bekenstein–Hawking entropy. Recently the extended uncertainty principle (EUP) and generalized extended uncertainty principle (GEUP) are introduced to calculate entropy corrections with large length scales limit. In this paper, we obtain the quantum corrections to Bekenstein–Hawking entropy in four-dimensional Schwarzschild black holes based on the EUP and GEUP. Some attractive results are derived.     

Quantum Corrections for Regular Black Holes with Charge and Coupling Constant

In this paper, we use semi-classical tunneling approach to calculate the quantum corrections to the Hawking temperature as well as entropy of the Kehagias-Sftesos asymptotically flat black hole solution and charged regular black hole with Fermi-Dirac distribution. For this purpose, we apply the first law of black hole thermodynamics to investigate the semi-classical entropy of both black holes having mass as well as charge or coupling constant. For both black holes, the entropy corrections contain the logarithmic term as a leading order correction term. For Kehagias-Sftesos asymptotically flat black hole, the semi-classical Hawking temperature and black hole entropy will behave asymptotically by considering the vanishing coupling constant b = 0. We have obtained the same analysis for the corrected thermodynamical quantities for this BH. For charged regular black hole with Fermi-Dirac distribution, if we neglect the charged effects in our analysis, i.e., q = 0, then these corrections approximately leads to the Schwarzschild black hole which is already given in the literature.     

Extremal static AdS black hole/CFT correspondence in gauged supergravities

A recently proposed holographic duality allows the Bekenstein–Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza–Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.     

A Planck-Like Problem for Quantum Charged Black Holes

Motivated by the parallelism existing between the puzzles of classical physics at the beginning of the XXth century and the current paradoxes in the search of a quantum theory of gravity, we give, in analogy with Planck's black body radiation problem, a solution for the exact Hawking flux of evaporating Reissner-Nordström black holes. Our results show that when back-reaction effects are fully taken into account the standard picture of black hole evaporation is significantly altered, thus implying a possible resolution of the information loss problem.