Black Hole Area Research Articles

A correction to the Immirzi parameter of [formula omitted] spin networks

The elegant predictions of loop quantum gravity are obscured by the free Immirzi parameter (γ). Dreyer (2003), considering the asymptotic quasinormal modes spectrum of a black hole, proposed that γ may be fixed by letting the j=1 transitions of spin networks as the dominant processes contributing to the black hole area, as opposed to the expected j=1/2 transitions. This suggested that the gauge group of the theory might be SO(3) rather than SU(2). Corichi (2003), maintaining SU(2) as the underlying gauge group, and invoking the principle of local fermion-number conservation, reported the same value of γ for j=1 processes as obtained by Dreyer. In this note, preserving the SU(2) structure of the theory, and considering j=1 transitions as the dominant processes, we point out that the value of γ is in fact twice the value reported by these authors. We arrive at this result by assuming the asymptotic quasinormal modes themselves as dynamical systems obeying SU(2) symmetry.

Deformations of Charged Axially Symmetric Initial Data and the Mass–Angular Momentum–Charge Inequality

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors [4] (arXiv:1401.3384), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass-angular momentum-charge inequality in the maximal case.

Area Spectrum of a Kerr-Newman Black Hole Via an Adiabatic Invariant

By virtue of a semiclassical adiabatic invariant in this paper, we quantize the horizon area of a Kerr-Newman black hole by making use of the period of the gravity system. We exploit exclusively the basic properties of the adiabatic invariant. It is found that the result produced by our method is consistent with the one obtained by calculating the adiabatic invariant step by step.

Deformations of Axially Symmetric Initial Data and the Mass-Angular Momentum Inequality

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which preserves the relevant geometry, while achieving the maximal condition and its implied inequality (in a weak sense) for the scalar curvature; this answers a question posed by R. Schoen. The primary equation involved, bears a strong resemblance to the Jang-type equations studied in the context of the positive mass theorem and the Penrose inequality. Each equation in the system is analyzed in detail individually, and it is shown that appropriate existence/uniqueness results hold with the solution satisfying desired asymptotics. Lastly, it is shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass and angular momentum.

Initiating the Effective Unification of Black Hole Horizon Area and Entropy Quantization with Quasi-Normal Modes

Black hole (BH) area quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In the specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of thestrictly thermal and nonstrictly thermalspectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, such work exemplifies a series of imperative corrections that eventually permits a BH’s horizon area spectrum to begeneralizedfrom strictly thermal to nonstrictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the results are significant because quasi-normal modes (QNM) and “effective states” characterize the transitions between the established levels of the nonstrictly thermal spectrum.

On Quasinormal modes and Quantization of Area of Black Holes

Perturbations of black holes give very important tools of understanding physical properties of black holes. The relaxation of the perturbation is described by quasinormal modes with complex frequency. Using this, there has been some proposal of Hod and later by Maggiore that one can obtain quantization of the area of black holes. These ideas, when applied to rotating black holes were less than controversial. In this work we address how the are can be quantized with equal spacing. We also comment on application of this to other black holes in three dimensional spacetime.

IS A GRAVITON DETECTABLE?

IS A GRAVITON DETECTABLE?

Einstein-Euler-Heisenberg theory and charged black holes

Taking into account the Euler-Heisenberg effective Lagrangian of one-loop nonperturbative quantum electrodynamics (QED) contributions, we formulate the Einstein-Euler-Heisenberg theory and study the solutions of nonrotating black holes with electric and magnetic charges in spherical geometry. In the limit of strong and weak electromagnetic fields of black holes, we calculate the black hole horizon radius, area, and total energy up to the leading order of QED corrections and discuss the black hole irreducible mass, entropy, and maximally extractable energy as well as the Christodoulou-Ruffini mass formula. We find that these black hole quantities receive the QED corrections, in comparison with their counterparts in the Reissner-Nordstr\"om solution. The QED corrections show the screening effect on black hole electric charges and the paramagnetic effect on black hole magnetic charges. As a result, the black hole horizon area, irreducible mass, and entropy increase; however, the black hole total energy and maximally extractable energy decrease compared with the Reissner-Nordstr\"om solution. In addition, we show that the condition for extremely charged black holes is modified due to the QED correction.

Lower bounds for the area of black holes in terms of mass, charge, and angular momentum

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.

Destroying the event horizon of regular black holes

Recently, several authors have studied the possibility of overspinning or overcharging an existing black hole to destroy its event horizon and make the central singularity naked. When all the effects are properly taken into account, any attempt to destroy the black hole seems to be doomed to fail, in agreement with the weak cosmic censorship conjecture. In this letter, we study the possibility of destroying the event horizon of regular black holes. These objects have no central singularity and therefore they are not protected by the cosmic censorship hypothesis. Our results strongly support the conclusion that regular black holes can be destroyed. If we believe that the central singularity in astrophysical black holes is solved by quantum gravity effects, we might have a chance to see the black hole's internal region and observe quantum gravity phenomena. As our finding implies the violation of the black hole's area theorem, the collision of two black holes may release an amount of energy exceeding the Hawking bound, which can be experimentally tested by gravitational wave detectors.

Area Spectra of d-Dimensional Extreme Reissner-Nordström Black Holes

With the physical interpretation of quasinormal modes proposed by Maggiore, we investigate the quantum area and entropy spectra of d-dimensional extreme Reissner-Nordstrom black holes. Employing two methods, the method of Maggiore and the action variable quantization, we arrive at the spectra consistent with each other. Results show that the spectra are irrelevant to the black hole parameters and the perturbation field parameters but relative to the spacetime dimension. For a given dimension, the spectra are equally spaced.

ERRATUM: "QUANTIZATION OF HIGHER-DIMENSIONAL LINEAR DILATON BLACK HOLE AREA/ENTROPY FROM QUASINORMAL MODES"

The quantum spectra of area and entropy of higher-dimensional linear dilaton black holes in various theories via the quasinormal modes method are studied. It is shown that quasinormal modes of these black holes can reveal themselves when a specific condition holds. Finally, we obtain that a higher-dimensional linear dilaton black hole has equidistant area and entropy spectra, and both of them are independent on the space–time dimension.

Generalized uncertainty principle and Bekenstein-Hawking entropy in tunneling rate of Kerr black hole

We study the effects of the generalized uncertainty principle in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature and entropy for a Kerr black hole. By assumption of a spatially flat universe accompanied with expansion of metric, the modified area and entropy of Kerr black hole are calculated and we could obtain an expression for entropy of black hole that is changing with respect to time and Bekenstein-Hawking temperature.

QUANTIZATION OF ENTROPY SPECTRA OF BLACK HOLES

From the quasinormal modes (QNM) of black holes, we obtain the quantizations of the entropy and horizon area of black holes via Bohr–Sommerfeld quantization, based on Bohr's correspondence principle. For this, we identify the appropriate action variable of the classical system corresponding to a black hole. By considering the BTZ black holes in topologically massive gravity as well as Einstein gravity, it is found that the spectra of not the horizon areas but the entropies of black holes are equally spaced. We also propose that other characteristic modes of black holes, which are non-QNM or holographic QNM, can be used in quantization of entropy spectra just like QNM. From these modes, it is found that only the entropy spectrum of the warped AdS3 black hole is equally spaced as well. Furthermore, by considering a scattering problem in a black hole, we propose that the total transmission modes and total reflection modes of black holes can be regarded as characteristic modes of black holes and result in the equally spaced entropy of the Kerr and Reissner–Nordström black holes. Finally, we conclude that there is a universal behavior that the entropy spectra of various black holes are equally spaced.

Galactic dark matter in the phantom field

We investigate the possibility that the galactic dark matter exists in an scenario where the phantom field is responsible for the dark energy. We obtain the statically and spherically approximate solution for this kind of the galaxy system with a supermassive black hole at its center. The solution of the metric functions is satisfied with $g_{tt} = - g_{rr}^{-1}$. Constrained by the observation of the rotational stars moving in circular orbits with nearly constant tangential speed in a spiral galaxy, the background of the phantom field which is spatially inhomogeneous has an exponential potential. To avoid the well-known quantum instability of the vacuum at high frequencies, the phantom field defined in an effective theory is valid only at low energies. Under this assumption, we further investigate the following properties. The absorption cross section of the low-energy $S$-wave excitations of the phantom field into the central black hole is shown to be the horizontal area of the central black hole. Because the infalling phantom particles have a total negative energy, the accretion of the phantom energy is related to the decrease of the black hole mass which is estimated to be much less than a solar mass in the lifetime of the Universe. Using a simple model with the cold dark matter very weakly coupled to the "{\it low-frequency}" phantom particles which are generated from the background, we show that these two densities can be quasi-stable in the galaxy.

On the nature of black holes in loop quantum gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum-mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes.

Influences of a Generalized Uncertainty Principle on the black-hole area spectrum in the tunneling formalism

In the Hawking's original semiclassical approach, the black-hole radiation is continuous. However, several authors have raised the interesting possibility that Hawking radiation might in fact have a discrete spectrum. Several calculations have been employed in order to find out the correct form of the black-hole area spectrum, but despite these efforts, this important issue remains unclear since we do not have yet a full theory of quantum gravity. In this article, we analyze the black-hole area spectrum through the use of the tunneling mechanism with a quantum gravity ingredient: the presence of a Generalized Uncertainty Principle (GUP). A discrete spectrum for the black-hole area is found out, and the presence of a GUP implies in a non-evenly spaced spectrum. The consequences for the micro black-hole luminosity are addressed.

Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity

We study quasi-stationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of gravitational theories.

Area and entropy spectra of black holes via an adiabatic invariant

By considering and using an adiabatic invariant for black holes, the area and entropy spectra of static spherically-symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.

Entropy spectrum of a Kerr anti-de Sitter black hole

The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equally spaced.