Hole Entropy Research Articles

Running boundary actions, Asymptotic Safety, and black hole thermodynamics

Previous explorations of the Asymptotic Safety scenario in Quantum Einstein Gravity (QEG) by means of the effective average action and its associated functional renormalization group (RG) equation assumed spacetime manifolds which have no boundaries. Here we take a first step towards a generalization for non-trivial boundaries, restricting ourselves to action functionals which are at most of second order in the derivatives acting on the metric. We analyze two examples of truncated actions with running boundary terms: full fledged QEG within the single-metric Einstein-Hilbert (EH) truncation, augmented by a scale dependent Gibbons-Hawking (GH) surface term, and a bi-metric truncation for gravity coupled to scalar matter fields. The latter contains 17 running couplings, related to both bulk and boundary terms, whose beta-functions are computed in the induced gravity approximation. We find that the bulk and the boundary Newton constant, pertaining to the EH and GH term, respectively, show opposite RG running; proposing a scale dependent variant of the ADM mass we argue that the running of both couplings is consistent with gravitational anti-screening. We describe a simple device for counting the number of field modes integrated out between the infrared cutoff scale and the ultraviolet. This method makes it manifest that, in an asymptotically safe theory, there are effectively no field modes integrated out while the RG trajectory stays in the scaling regime of the underlying fixed point. As an application, we investigate how the semiclassical theory of Black Hole Thermodynamics gets modified by quantum gravity effects and compare the new picture to older work on `RG-improved black holes' which incorporated the running of the bulk Newton constant only. We find, for instance, that the black hole's entropy vanishes and its specific heat capacity turns positive at Planckian scales.

Quantum geometry and entanglement entropy of a black hole

We have studied here black hole entropy in the framework of quantum geometry. It is pointed out that the black hole radiation consistent with Hawking spectrum can be realized as an effect of quantum geometry using a dynamical formalism for diffeomorphism invariance which envisages a discretized unit of time in the Planck scale. This formalism suggests that torsion acts within a quantized area unit (area bit) associated with a loop and this eventually forbids the Hamiltonian constraint to be satisfied for a finite loop size. We assign a spin with torsion in each area bit and entanglement entropy of a black hole is computed in terms of the entanglement entropy of this spin system. We have derived the Bekenstein-Hawking entropy along with a logarithmic correction term with a specific coefficient. Also we have shown that the Bekenstein-Hawking entropy can be formulated in terms of the Noether charge associated with a diffeomorphism invariant Lagrangian.

MODIFIED DISPERSION RELATIONS: FROM BLACK-HOLE ENTROPY TO THE COSMOLOGICAL CONSTANT

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.

Correction to the Dirac field entropy of a Schwarzschild black hole by a modified dispersion relation

Taking the WKB approximation to solve the Dirac field equation in a Schwarzschild black hole spacetime, we can get the classical momenta. Employing the classical momenta and state density equation corrected by a modified dispersion relation, we will obtain the number of quantum states with energy less than $\ensuremath{\omega}$. Then, it is used to calculate the statistical-mechanical entropy of the Dirac field. Solving the integral for $r$ exactly, we obtain the leading term of entropy that is proportional to the event horizon area, and correction terms take the form of ${A}^{\ensuremath{-}1}$, but the logarithmic correction term by this approach is not given.

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.

Cardy-Verlinde Formula and Thermodynamics of Dilaton-axion Black Hole

In this paper, we have shown that the entropy of the dilaton-axion black hole can be expressed by the Cardy-Verlinde formula. The later is supposed to be an entropy formula of conformal field theory in any dimension. Next we have calculated the first order correction to the Cardy-Verlinde formula in the context of dilaton-axion black hole.

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.

A NEAR-NHEK/CFT CORRESPONDENCE

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U (1)L × U (1)R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and nonvanishing and find the central charges cL = 12J/ℏ and cR = 0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a nonchiral two-dimensional conformal field theory.

Black Hole Horizons and Thermodynamics: A Quantum Approach

We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r0. After imposing spherical symmetry and after restriction to the Killing horizon, the metric is quantized employing the chiral currents formalism. Two "components of the metric" are indeed quantized: The former behaves as an affine scalar field under changes of coordinates, the latter is instead a proper scalar field. The action of the symplectic group on both fields is realized in terms of certain horizon diffeomorphisms. Depending on the choice of the vacuum state, such a representation is unitary. If the reference state of the scalar field is a coherent state rather than a vacuum, spontaneous breaking of conformal symmetry arises and the state contains a Bose-Einstein condensate. In this case the order parameter fixes the actual size of the black hole with respect to r0. Both the constructed state together with the one associated with the affine scalar are thermal states (KMS) with respect to Schwarzschild Killing time when restricted to half horizon. The value of the order parameter fixes the temperature at the Hawking value as well. As a result, it is found that the quantum energy and entropy densities coincide with the black hole mass and entropy, provided the universal parameter r0 is suitably chosen, not depending on the size of the actual black hole in particular.

Hawking Radiation from Charged Kerr Black Hole Beyond Semi-classical Approximation

The Hawking radiation from charged Kerr black hole via the method beyond semi-classical approximation is studied. In our work, we apply the WKB approximation method and the quantum tunneling method, then calculate the tunneling rate and further correct Hawking entropy to charged Kerr black hole. It is shown that the result is still in agreement with the unitary theory, the entropy of the black hole contains three parts: the usual Bekenstein-Hawking entropy, the logarithmic term and the inverse area term. Apart from coefficients, our correction to the charged Kerr black hole entropy is consistent with results of loop quantum gravity.

A bound on the entropy of supergravity?

We determine, in two independent ways, the number of BPS quantum states arising from supergravity degrees of freedom in a system with fixed total D4D0 charge. First, we count states generated by quantizing the spacetime degrees of freedom of 'entropyless' multicentered solutions consisting of anti-D0-branes bound to a D6-anti-D6 pair. Second, we determine the number of free supergravity excitations of the corresponding AdS_3 geometry with the same total charge. We find that, although these two approaches yield a priori different sets of states, the leading degeneracies in a large charge expansion are equal to each other and that, furthermore, the number of such states is parametrically smaller than that arising from the D4D0 black hole's entropy. This strongly suggests that supergravity alone is not sufficient to capture all degrees of freedom of large supersymmetric black holes. Comparing the free supergravity calculation to that of the D6-anti-D6-D0 system we find that the bound on the free spectrum imposed by the stringy exclusion principle (a unitarity bound in the dual CFT) seems to be captured in the dynamics of the fully interacting but classcial supergravity equations of motion.

Holographic entropy of Gibbons-Maeda dilaton black hole

In accordance with the holographic principle， by calculating the entropy of the quantum field just on the event horizon of the Gibbons-Maeda dilaton black hole， the holographic entropy and the Bekenstein-Hawking entropy of the black hole are obtained. By using the non-commutative quantum field theory， the divergence of the state density near the event horizon in usual quantum field theory is removed and the ultraviolet cutoff in the heat gas method of black hole entropy is avoided.Using the residue theorem, the integral difficulty in the calculation is overcome and the results here are obtained quantitatively. The results show that black hole entropy is identical with the statistical entropy of the quantum states at the horizon. Black hole entropy may be obtained by calculating the quantum states only at the event horizon, and in the calculation the influences of quantum states outside the horizon should be avoided.

Corrections to Hawking radiation from the black hole surrounded by quintessence

In this paper, using the Hamilton-Jacobi method beyond semiclassical approximation in black hole physics which was developed by Banerjee and Majhi, we compute the temperature and entropy of the black hole surrounded by quintessence and obtain the corrected temperature and entropy. In the corrected entropy, the area law involves logarithmic area correction together with the standard inverse power of area term.

Black hole evaporation within a momentum-dependent metric

We investigate the black hole thermodynamics in a ``deformed'' relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cutoff. We obtain net deviations of the basic thermodynamical quantities from the Hawking-Bekenstein predictions: actually, the black hole evaporation is expected to quit at a nonzero critical mass value (of the order of the Planck mass), leaving a zero temperature remnant, and avoiding a spacetime singularity. Quite surprisingly, the present semiclassical corrections to black hole temperature, entropy, and heat capacity turn out to be identical to the ones obtained within some quantum approaches.

A new approach to two-charge fuzzball geometries

A few years ago, Mathur proposed a ‘fuzzball’ conjecture to give a microscopic description of black hole entropy. In the fuzzball scenario, the entropy in a two-charge black hole corresponds to microstates of a two-charge string (brane) system, e.g., a winding fundamental string with momentum modes. The geometry of such a two-charge system is fuzzy near the horizon, and is very difficult to get analytically in general. In this paper, we show a new method to get geometries of two-charge fuzzball. Our method is based on the multipole expansion. We find that the method is powerful enough to get a clean analytic form of metric of the fuzzball with one-momentum mode. It is expected to get multi-mode geometries using this method in the near future.

Thermodynamics Properties of the Inner Horizon of a Kerr-Newman Black Hole

In this paper, we study the thermal properties of the inner horizon of a Kerr-Newman black hole. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a Kerr-Newman black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. The cut-off factor is same as it in calculation of the entropy of the outer horizon, 90β. In addition, we write the integral and differential Bekenstein-Smarr formula as the parameters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, We calculate the tunneling rate of the outer horizon Γ+ and the inner horizon Γ−. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ+⋅Γ−. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔSBH), and there is no information loss.

Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ+ and the inner horizon Γ−. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ+⋅Γ−. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS BH ), and there is no information loss.

Holographic dark energy: Quantum correlations against thermodynamical description

Classical and quantum entropic properties of holographic dark energy (HDE) are considered in view of the fact that its entropy is far more restrictive than the entropy of a black hole of the same size. In cosmological settings (in which HDE is promoted to a plausible candidate for being the dark energy of the universe), HDE should be viewed as a combined state composed of the event horizon and the stuff inside the horizon. By any interaction of the subsystems, the horizon and the interior become entangled, raising thereby a possibility that their quantum correlations be responsible for the almost purity of the combined state. Under this circumstances, the entanglement entropy is almost the same for both subsystems, being also of the same order as the thermal (coarse grained) entropy of the interior or the horizon. In the context of thermodynamics, however, only additive coarse grained entropies matter, so we use these entropies to test the generalized second law (GSL) of gravitational thermodynamics in this framework. While we find that the original Li's model passes the GSL test for a special choice of parameters, in a saturated model with the choice for the IR cutoff in the form of the Hubble parameter, the GSL always breaks down.

Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length

Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.

GENERALIZED UNCERTAINTY PRINCIPLE AND THERMODYNAMIC QUANTITIES OF THE ACHUCARRO–ORTIZ BLACK HOLE

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of a black hole. In this paper, we calculate the correction value of thermodynamic quantities of the Achucarro–Oritz black hole motivated by utilizing the generalized uncertainty principle. We obtain the Cardy–Verlinde formula after considering the correction.