Black Hole Area Research Articles

Black hole motion in Euclidean space as a diffusion process

A diffusion equation for a black hole is derived from the Bunster-Carlip equations. Its solution has the standard form of a Gaussian distribution. The second moment of the distribution determines the quantum of black hole area. The entropy of diffusion process is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy.

Generalized uncertainty principle and s-wave semiclassical tunneling radiation of Kerr black hole

Based on the generalized uncertainty principle, the modified area and entropy of Kerr black hole is calculated. The semiclassical Parikh-Wilczeck tunneling proposal is applied to a Kerr horizon. It is shown that the tunneling radiation probability of Kerr black hole is modified.

GRAVITATIONAL COLLAPSE AND BLACK HOLE THERMODYNAMICS IN BRANEWORLD SCENARIO

We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner–Nordstrom solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics for quasi-extremal configurations, with an extra work term in the laws associated with variations of the brane tension. We also propose a simple statistical mechanics model for the entropy of the bouncing collapsed matter by quantizing its fluctuations and constructing the associated partition function. This entropy differs from the geometrical entropy by an additive constant proportional to the area of the extremal black hole and satisfies an analogous first law of thermodynamics. A possible connection between both entropies is discussed.

Statistical entropy of reissner-nordstrm-de sitter black hole by generalized uncertainty principle

Statistical entropy of scalar field outside Reissner-Nordstrm-de Sitter black hole is computed by the equation of state density corrected by the generalized uncertainty principle and by Wentzel-Kramers-Brillouin approximation method. The result shows that the entropy is proportional to the sum of the internal, the external and the cosmological horizon areas, which accords with these calculated by other methods. It shows internal relation between the entropy of black hole and horizon area. The entropy of black hole is the entropy of quantum state on horizon, which is a quantum effect.

BLACK HOLE AREA SPECTRUM AND ENTROPY SPECTRUM VIA QUASINORMAL MODES IN A QUANTUM CORRECTED SPACETIME

The area spectrum and entropy spectrum of the modified Schwarzschild black hole in gravity's rainbow are investigated via the quasinormal modes of the black hole. Using the modified Hod's method and Kunstatter's method that employ the proper frequency from the imaginary part other than the real part of the quasinormal modes, the area and entropy spacing of the black hole are calculated. The results obtained from these two methods agree with each other and the equally spaced area and entropy spectrum are derived. The obtained area and entropy spectrum are independent of the energies of test particles and are the same as from the usual Schwarzschild black hole.

Black hole area–angular-momentum inequality in nonvacuum spacetimes

We show that the area-angular-momentum inequality $A\ensuremath{\ge}8\ensuremath{\pi}|J|$ holds for axially symmetric closed outermost stably marginally trapped surfaces. These are horizon sections (in particular, apparent horizons) contained in otherwise generic non-necessarily axisymmetric black hole spacetimes, with a non-negative cosmological constant and whose matter content satisfies the dominant energy condition.

Black Hole Evaporation Rates without Spacetime

Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high dimensionality of black holes, global conservation of the no-hair quantities, and the existence of Penrose processes. Our analysis is not wedded to standard general relativity and so should apply to extended gravity theories where we find that the black hole area must be replaced by some other property in any generalized area theorem.

Minimal length and black hole area quantization

AbstractIn this talk we discuss implications of the concept of the minimal length, the Planck length, for black hole physics, and argue, that it naturally leads to quantization of black hole area in Planck units.

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.

The Quantum Formulation of Black Hole Area Spectrum and Entropy Spectrum

In this paper, the area spectrum of this static BTZ black hole in different cases (rotating, non-rotating, and extreme) is investigated. The final results show that the spectral formulation is 2πnℏ when this black hole is non-rotating. For the black hole in other two different cases, its spectrum is angular momentum-dependent. Unexpectedly, their area spectra are both equally spaced. What is more, the entropy spectrum is also calculated via the method put forward by Chen et al. However, it is demonstrated that the well known area-entropy law is greatly changed. Above all, the entropy spectrum of this non-rotating BTZ black hole is also equally spaced.

AREA SPECTRUM OF THE EXTREME REISSNER–NORDSTRÖM BLACK HOLE

Motivated by the new interpretation on quasinormal modes by Maggiore, we investigate the quantization of the extreme Reissner–Nordström black hole in the four-dimensional spacetime. Following Kunstatter's method, we derive the equally spaced area spectrum and the entropy, however the spacing differs from Setare's result via Hod's proposal. Moreover, our result is in full agreement with Bekenstein's result as well as the claim that black hole's area is equidistant in Einstein's Gravity theory by Wei et al.

Thermodynamics of magnetized binary compact objects

Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically symmetric perfect-fluid spacetimes are extended to include the electromagnetic fields, and electric currents and charges; the first law is written as a relation between the change in the asymptotic Noether charge $\ensuremath{\delta}Q$ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetized fluid. Using the conservation laws of the circulation of magnetized flow found by Bekenstein and Oron for the ideal magnetohydrodynamic fluid, and also for the flow with zero conducting current, we show that, for nearby equilibria that conserve the quantities mentioned above, the relation $\ensuremath{\delta}Q=0$ is satisfied. We also discuss a formulation for computing numerical solutions of magnetized binary compact objects in equilibrium with emphasis on a first integral of the ideal magnetohydrodynamic-Euler equation.

Area spectra versus entropy spectra of black holes in topologically massive gravity

The area and entropy spectra of black holes in topologically massive gravity with the gravitational Chern–Simons term are calculated. The examples we consider are the BTZ black hole and the warped AdS3 black hole. For the non-rotating BTZ black hole, we find that the gravitational Chern–Simons term does not affect the area and entropy spectra, so that they are equally spaced. For the rotating BTZ black hole, the spectra of the inner and outer horizon areas are not equally spaced and dependent on the coupling constant ν of the gravitational Chern–Simons term. However the entropy spectrum is equally spaced and independent of the coupling constant ν. For the warped AdS3 black hole, we again find that the entropy spectrum is equally spaced and independent of the coupling constant ν, while the spectra of the inner and outer horizon areas are not equally spaced and dependent on the coupling constant ν. Our result implies that the entropy spectrum has a universal behavior regardless of the presence of the gravitational Chern–Simons term, and therefore the entropy is more ‘fundamental’ than the horizon area. We propose to use this universal behavior of the entropy spectrum as criteria of a correct quasinormal mode.

Area Spectrum of D-Dimensional Large Schwarzschild-AdS Black Hole from Asymptotic Quasinormal Modes

We investigate the area and entropy spectra of D-dimensional large Schwarzschild black holes. By utilizing the new physical interpretation of quasinormal mode frequency we find that a large Schwarzschild-AdS black hole has an equally spaced area spectrum and an equidistant entropy spectrum; both are dependent on the spacetime dimension.

Torsion effects in braneworld scenarios

We present gravitational aspects of braneworld models endowed with torsion terms both in the bulk and on the brane. In order to investigate a conceivable and measurable gravitational effect, arising genuinely from bulk torsion terms, we analyze the variation in the black hole area by the presence of torsion. Furthermore, we extend the well known results about consistency conditions in a framework that incorporates brane torsion terms. It is shown, in a rough estimate, that the resulting effects are generally suppressed by the internal space volume. This formalism provides manageable models and their possible ramifications into some aspects of gravity in this context, and cognizable corrections and physical effects as well.

A heuristic analysis of black hole thermodynamics with generalized uncertainty principle

In the standard viewpoint, the temperature of a stationary black hole is proportional to its surface gravity. This is a semiclassical result and the quantum gravity effects are not taken into consideration. This research explores a unified expression for the black hole temperatures in the sense of a generalized uncertainty principle (GUP). Our argument is based on a heuristic analysis of a particle which is absorbed by the black hole. We make a new proposal that the square root of the black hole area represents the characteristic size in the absorption process (i.e. ρ0 ~ A1/2), which is valid to a class of static and spherically symmetric black holes and a Kerr-Newman case. The information capacity of a remnant is also discussed by Bousso's D-bound in de Sitter spacetime.

Quantization of the black hole area as quantization of the angular momentum component

In transforming from Schwarzschild to Euclidean Rindler coordinates the Schwarzschild time transforms to a periodic angle. As is well-known, this allows one to introduce the Hawking temperature and is an origin of black hole thermodynamics. On the other hand, according to quantum mechanics this angle is conjugate to the $z$ component of the angular momentum. From the commutation relation and quantization condition for the angular momentum component it is found that the area of the horizon of a Schwarzschild black hole is quantized with the quantum $\ensuremath{\Delta}A=8\ensuremath{\pi}{l}_{P}^{2}$. It is shown that this conclusion is also valid for a generic Kerr-Newman black hole.

Black Hole Entropy with Modified Dispersion Relations

There is much interest in resolving the quantum corrections to Bekenstein–Hawking entropy with a large length scale limit. The leading correction term is given by the logarithm of black hole area with a model-dependent coefficient. Recently the research for quantum gravity implies the emergence of a modification of the energy-momentum dispersion relation (MDR), which plays an important role in the modified black hole thermodynamics. In this paper, we investigate the quantum corrections to Bekenstein–Hawking entropy in four-dimensional Schwarzschild black hole and Reissner–Nordström black hole respectively based on MDR.

Accretion of phantom scalar field into a black hole

Using numerical methods we present the first full nonlinear study of phantom scalar field accreted into a black hole. We study different initial configurations and find that the accretion of the field into the black hole can reduce its area down to 50 percent within time scales of the order of few masses of the initial horizon. The analysis includes the cases where the total energy of the space-time is positive or negative. The confirmation of this effect in full nonlinear general relativity implies that the accretion of exotic matter could be considered an evaporation process. We speculate that if this sort of exotic matter has some cosmological significance, this black hole area reduction process might have played a crucial role in black hole formation and population.

Black holes in asymptotically Lifshitz spacetime

A model of 3+1 dimensional gravity with negative cosmological constant coupled to abelian gauge fields has been proposed as a gravity dual for Lifshitz like critical phenomena in 2+1 dimensions. The finite temperature behavior is described by black holes that are asymptotic to the Lifshitz fixed point geometry. There is a one-parameter family of charged black holes, where the magnitude of the charge is uniquely determined by the black hole area. These black holes are thermodynamically stable and become extremal in the limit of vanishing size. The theory also has a discrete spectrum of localized objects described by non-singular spacetime geometries. The finite temperature behavior of Wilson loops is reminiscent of strongly coupled gauge theories in 3+1 dimensions, including screening at large distances.