Narrow Results

Hawking radiation emanating from two-dimensional charged and uncharged dilatonic black holes — dimensionally reduced from (2+1) spinning and spinless, respectively, BTZ black holes — is viewed as a tunneling process. Two-dimensional dilatonic black holes (AdS(2) included) are treated as dynamical background in contrast to the standard methodology where the background geometry is fixed when evaluating Hawking radiation. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. Nonzero temperature of the extremal two-dimensional charged black hole is found. The Bekenstein–Hawking area formula is easily derived for these dynamical geometries.

The quantum entropies of the black hole, due to the massless Klein–Gordon and Dirac fields, are investigated by Rindler approximation. The difference from the brick wall model is that we take into account the effect of the generalized uncertainty relation on the state counting. The divergence appearing in the brick wall model is removed and the entropies proportional to the horizon area come from the contributions of the modes in the vicinity of the horizon. Here we take the units G=c=ℏ=k_B=1.

In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent) notion of entropy with the horizon that blocks the information from these observers. While the blockage of information is absolute in classical physics, quantum mechanics will allow tunnelling across the horizon. This process can be analyzed in a simple, yet general, manner and we show that the probability for a system with energy E to tunnel across the horizon is P(E)∝exp[-(2π/κ)E) where κ is the surface gravity of the horizon. If the surface gravity changes due to the leakage of energy through the horizon, then one can associate an entropy S(M) with the horizon where dS=[2π/κ(M)]dM and M is the active gravitational mass of the system. The implications are discussed.

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.

Black-holes are considered to be theoretical laboratories for testing models of quantum gravity. It is usually believed that any candidate for quantum gravity must explain the microscopic origin of the Bekenstein–Hawking (S_BH) entropy. In this letter, we argue (i) the requirement for a candidate approach to go beyond S_BH and provide generic subleading corrections, and (ii) the importance to disentangle and identify the degrees of freedom leading to S_BH and its subleading corrections. Using the approach of entanglement of modes across the horizon, we show that the microscopic degrees of freedom that lead to S_BH and subleading corrections are different. We further show, using microcanonical and canonical ensemble approaches, that the quantum entanglement predicts generic power-law corrections to S_BH and that the corrections can be identified with the kinematical properties of the event-horizon.

We study the entropy of extremal warped black hole obtained from the topologically massive gravity with a negative cosmological constant of Λ = -1/l². We compare the entropy S_e = πα/3G from the Wald formalism with S_w = πl u /3G from the entropy function approach. These are the same if α = l u. Also we obtain the same Cardy formula when J_e = l³ q with J_e the angular momentum and q the conserved quantity.

There has been much debate about the form of the quantum area spectrum for a black hole horizon, with the evenly spaced conception of Bekenstein having featured prominently in the discourse. Here, we refine a very recently proposed method for calibrating the Bekenstein form of the spectrum. Our refined treatment predicts, as did its predecessor, a uniform spacing between adjacent spectral levels of 8π in Planck units — notably, an outcome that already has a pedigree as a proposed "universal" value for this intrinsically quantum-gravitational measure. Although the two approaches are somewhat similar in logic and quite agreeable in outcome, we argue that our version is conceptually more elegant and formally simpler than its precursor. Moreover, our rendition is able to circumvent a previously unnoticed technical issue and, as an added bonus, translates to generic theories of gravity in a very direct manner.

It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons, as perceived by the local Rindler observer, play a crucial role in this approach. In this context, the relation S = E/2T between the entropy (S), active gravitational mass (E) and temperature (T) — obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] — can be reinterpreted as the law of equipartition E = (1/2) nk_BT where is the number (density) of microscopic horizon degrees of freedom in an area ΔA. Conversely, one can use the equipartition argument to provide a thermodynamic interpretation of gravity, even in the nonrelativistic limit. These results emphasize the intrinsic quantum nature of all gravitational phenomena and diminishes the distinction between thermal phenomena associated with local Rindler horizons and the usual thermodynamics of macroscopic bodies in non-inertial frames. Just like the original thermodynamic interpretation, these results also hold for a wide class of gravitational theories like the Lanczos–Lovelock models.

In the tunneling framework of Hawking radiation, the quantum tunneling of massive particles in the modified Schwarzschild black holes from gravity's rainbow is investigated. While the massive particle tunneling from the event horizon, the metric fluctuation is taken into account, not only due to energy conservation but also to the Planck scale effect of spacetime. The obtained results show that, the emission rate is related to changes of the black hole's quantum corrected entropies before and after the emission. This implies that, considering the quantum effect of spacetime, information conservation of black holes is probable. Meanwhile, the quantum corrected entropy of the modified black hole is obtained and the leading correction behave as log-area type. And that, the emission spectrum with Planck scale correction is obtained and it deviates from the thermal spectrum.

Starting from a quantization relation for primordial extremal black holes with electric and magnetic charges, it is shown that their entropy is quantized. Furthermore, the energy levels spacing for such black holes is derived as a function of the level number n, appearing in the quantization relation. Some interesting cosmological consequences are presented for small values of n. By producing a mismatch between the mass and the charge, the black hole temperature is derived and its behavior investigated. Finally extending the quantum relation to Schwarzschild black holes their temperature is found to be in agreement with the Hawking temperature and a simple interpretation of the microscopic degrees of freedom of the black holes is given.

Various proposals for gravitational entropy densities have been constructed from the Weyl tensor. In almost all cases, though, these studies have been restricted to general relativity, and little has been done in modified theories of gravity. However, in this paper, we investigate the simplest proposal for an entropy density constructed from the Weyl tensor in five-dimensional Gauss–Bonnet gravity and find that it fails to reproduce the expected entropy of a black hole.

In this paper, we take the view that the area of a black hole’s event horizon is quantized, $A=l_P^2(4ln2)N$, and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, $S_{\mathrm{\text{BH}}}$, our main focus being black hole self-similarity. We first find a two-to-one map between the black hole’s configurations and the ordered partitions of the integer $N$. Hence, we construct from there a composition law between the subparts making the whole configuration space. This gives meaning to black hole self-similarity, entirely within a single description, as a phenomenon stemming from the well-known self-similarity of the ordered partitions of $N$. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, which necessarily require different (quantum) statistical weights for the various configurations.

By introducing a new Tortiose coordinate and using the notion of local equilibrium, we have studied the Hawking effect and the entropy of an arbitrarily accelerating Kerr black hole, a nonstationary black hole. The Bekenstein–Hawking entropy has been obtained by taking the same geometric cutoff relationship in the thin film model as that in the static case. Consequently, the results in the new Tortiose coordinate reveal the following two facts. First, it is correct in the opinion that the black hole entropy is determined by the horizon of a black hole, whether it is stationary or nonstationary. Second, the entropy of the nonstationary black hole shows some common essential natures with that of a static one.

An intriguing question related to black hole thermodynamics is that the entropy of a region shall scale as the area rather than the volume. In this essay we propose that the microscopical degrees of freedom contained in a given region of space, are statistically related in such a way that obey a nonstandard statistics, in which case an holographic hypothesis would not be needed. This could provide us with some insight about the nature of degrees of freedom of the geometry and/or the way in which gravitation plays a role in the statistic correlation between the degrees of freedom of a system.

The black hole entropy due to spin fields are calculated by using brick-wall model. The appearance of the logarithmic terms is demonstrated and we specially deal with the subleading logarithmic term which exists for any spin fields. It is shown that the subleading logarithmic term is related to the use of WKB approximation but it usually includes not only a quadratic term and a linear term of the spin but also a zero-power term of the spin.

It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer–Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.

We holographically derive entropy of (near) extremal black holes as entanglement entropy of conformal quantum mechanics(CQM) living in two boundaries of AdS₂.

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS₂/CFT₁ correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry — named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.

By making use of the grasping action of the area operator as an antisymmetrizer of the grasped strands in spin network and the Penrose binor identity, an equidistant area spectrum is deduced. Utilizing the spectrum to calculate the quantized area of black hole horizon, we recalculate the entropy of black hole H(A) = (8πℏG_N)^-1kA ln 2. By taking advantage of the smallest area quantum "½" excited by the spectrum via the Wilson loop in edge of spin network to approach the possible origin of qubit, the existences of entanglement of the area quanta in quantum space, as well as the nonlocal property of the entangled states are demonstrated.

Black holes with multi-horizons may provide new ways to understand the intrinsic thermodynamics. In this work, we focus on the entropy relations of black holes in three, four and higher dimensions. These entropy relations include entropy product, "part" entropy product and entropy sum. We also discuss their differences and similarities, in order to make a further study on understanding the origin of black hole entropy at the microscopic level.