Hole Entropy Research Articles

Entropy of toroidal black hole to all orders in the Planck length

Entropy of toroidal black hole to all orders in the Planck length

The information entropy of a static dilaton black hole

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

Entropy of the scalar field in general accelerating non-stationary black holes with electric charge and magnetic charge

Using tortoise coordinate transformation, Klein-Gordon field equation is simplified and thermal radiation temperature near the event horizon is obtained. Meanwhile, adopting thin film brick-wall model and regulating the cut-off parameter and the thin film's thickness properly, the entropy of thin film near the event horizon is acquired. The results show that the entropy of the black hole is proportional to the area of the event horizon.

Quantum statistical entropy of axisymmetric black hole

Using the quantum statistical method, the difficulty of solving wave equation on the background of the black hole is avoided. We directly solve the partition functions of bosonic field and fermionic field on the background of the axisymmetric Kerr black hole through using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity theory. Then the entropy of the bosonic field and fermionic field near the horizon of the black hole are calculated. In our results the divergence appearing in the brick wall model is removed, as well as without using the small mass approximation. The series expression of the statistical entropy of the black hole is convergent. Therefore, it gives a better understanding of the black hole statistical entropy in non-spherical symmetry spacetimes.

GENERAL LOGARITHMIC CORRECTIONS TO BEKENSTEIN–HAWKING ENTROPY

Recently, there has been a lot of attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of the black hole. In particular, the coefficient of the logarithmic term in the black hole entropy correction has been of great interest. In this paper, the black hole is corresponded to a canonical ensemble in statistics by radiant spectrum, resulted from the black hole tunnelling effect studies and the partition function of ensemble is derived. Then the entropy of the black hole is calculated. When the first-order approximation is taken into account, the logarithmic term of entropy correction is consistent with the result of the generalized uncertainty principle. In our calculation, there are no uncertainty factors. The prefactor of the logarithmic correction and the one if fluctuation is considered are the same. Our result shows that if the thermal capacity is negative, there is no divergent term. We provide a general method for further discussion on quantum correction to Bekenstein–Hawking entropy. We also offer a theoretical basis for comparing string theory and loop quantum gravity and deciding which one is more reliable.

Microstate Counting of 3-charge Black Hole from Supergravity

where A is the area of the horizon. Statistical mechanics then suggests that there should be e states of the black hole, but the geometry of the black hole is completely determined by its mass, charge and angular momentum : so called ‘Black holes have no hair’. This statement implies that the entropy of the black hole is S = ln 1 = 0. This is the ‘black hole entropy puzzle’, which is closely related to the ‘black hole information problems’. String theory has a rich structure and admits black-hole solutions in higher dimensions [2–4]. Then, the black holes in string theory may give an understanding of these puzzles. Black holes in string theory are widely studied by using a chiral null model [5–11]. This model provides a class of exact solutions of oscillating strings in various cases. From these solutions, Mathur proposed the ‘fuzzy ball’ conjecture for the black hole [12,13]. He constructed a geometry of the two-charge black hole by performing a chain of duality transformations from the metric of the oscillating fundamental string. The result gives a family of geometries for the D1-D5 system characterized by a single function ~ F , the vibration profile of the fundamental string. Moreover these geometries have no horizons and no singularity which corresponds to the so-called ‘black hole microstate geometries’. By quantizing the single function ~ F , we can obtain the number of geometries for the black hole [14]. This result agrees with the one from the calculation in the CFT side.

Calculating Entropy of Plane Symmetry Black Hole via Generalized Uncertainty Relation

The generalized uncertainty relation is introduced to calculate entropy of the black hole. By using quantum statistical method, we directly obtain the partition function of Bose and Fermi field on the background of the plane symmetry black hole. Then we calculate the entropy of Bose and Fermi field on the background of black hole near the horizon of the black hole. In our calculation, we need not introduce cutoff. There are not the left out term and the divergent logarithmic term in the original brick-wall method. And it is obtained that the entropy of the black hole is proportional to the area of the horizon. The inherent contact between the entropy of black hole and the area of horizon is opened out. Further it is shown the entropy of black hole is entropy of quantum state on the surface of horizon. The black hole’s entropy is the intrinsic property of the black hole. The entropy is a quantum effect.

Entropy of Dirac field in a rectilinearly nonuniformly accelerating Kinnersley black hole

Using the Tortoise coordinate transformation and the Dirac field equation near the event horizon, the Hawking temperature of Kinnersley black hole is obtained. Meanwhile, adopting thin film brick-wall model, the entropy of Kinnersley black hole is calculated. The entropy near the event horizon is shown to be the entropy of black hole by regulating the cut-off parameter and the thin film's thickness properly. The results show that the entropy of the black hole is proportional to the area of the event horizon.

Canonical entropy of black hole

Recently, Hawking radiation of the black hole was studied by tunnel effect method. It was found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How the deviation between the radiation spectrum from pure thermal spectrum affect the entropy is a very interesting problem. In this paper, we calculate the partition function using the energy spectrum derived by tunnel effect, then obtain the entropy of the black hole. When we take first order approximation, the logarithmic term of entropy correction is consistent with the one considering the generalized uncertainty relation. However, in our calculation, there is no uncertain factor. And the coefficient of logarithmic correction term is the same one after considering the correction to the black hole entropy due to the thermal fluctuation. There are no divergent terms in our result when the thermal capacity of the black hole is negative. So our discussion has universality.

Logarithmic terms in brick wall model

Abstract We clarify the relation between black hole entropy and quantum field spin. Starting from the Newman–Penrose formalism, we derive the Teukolsky-type master equation governing massless fields of arbitrary spin s ⩽ 2 in the Kerr–Newman–de Sitter spacetime. Then using the 't Hooft's brick wall model, we calculate the entropy of the black hole due to the quantum fields by the WKB approximation on the Teukolsky-type master equation. In particular, we carefully deal with the logarithmic term contribution to the entropy. It is shown that the term not only depends on the characteristics of the metric and the quadratic term of quantum field spin but also on the linear term of quantum field spin. This is very different from the result obtained earlier. All results of the present work are valid for the Schwarzschild, Reissner–Nordstrom, Kerr, Kerr–Newman, and de Sitter spacetime background, or any combination of these.

Entropy function for 4-charge extremal black holes in type IIA superstring theory

We calculate the entropy of 4-charge extremal black holes in Type IIA supersting theory by using Sen's entropy function method. Using the low-energy effective actions in both 10D and 4D, we find precise agreements with the Bekenstein-Hawking entropy of the black hole. We also calculate the higher-order corrections to the entropy and find that they depend on the exact form of the higher-order corrections to the effective action.

The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

Using the thin film brick-wall model,taking into account the effect of the generalized uncertainty principle on the equation of the density of the states, we calculate the free energy and entropy of schwarzschild black hole due to scalar field, we obtain the entropy proportional to the event horizon area without cutoff. This implies that quantum theory of gravity can remove the divergence of the state density on the event horizon and avoid the cutoff in the original brick-wall model, these results also mean that the thin film brick-wall model is universal.

Dispersion relation, black hole thermodynamics and generalization of uncertainty principle

Abstract In a heuristic manner, we discuss the effect of the modified dispersion relation (MDR) on the thermodynamics of a Schwarzschild black hole (including the corrections to black hole temperature and entropy). Different from the generalized uncertainty principle (GUP), the linear-in- l p term of MDR provides a correction of order of the square root of the black hole area, besides a logarithmic correction. MDR may be constrained to a certain extent. The relation between MDR and GUP is also discussed.

Deformed Density Matrix and Quantum Entropy of the Black Hole

In the present work the approach - density matrix deformation - earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales) is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.

Entropy of Dirac field in a generalized non-stationary spherically symmetric black hole with charge

Using the improved brick-wall film model， we calculated the entropy of Dirac field in a generalized non-stationary spherically symmetric black hole with charge. From the point of view of the model， these entropies are nothing but the entropy of the black hole. The result showed that this entropy is proportion to the area of event horizon.

GRAVITATIONAL UNCERTAINTY AND BLACK HOLE REMNANTS

Possible existence of black holes remnants provides a suitable candidates for dark matter. In this paper we study the possibility of existence for such remnants. We consider quantum gravitational induced corrections of black hole's entropy and temperature to investigate the possibility of such relics. Observational scheme for detection of these remnants and their cosmological constraints are discussed.

PARTICLE TUNNELS FROM GARFINKLE–HORNE BLACK HOLE AND HOROWITZ–STROMINGER BLACK HOLE

When the black hole radiates particles, it losses energy and shrinks, it is the contraction of the horizon that sets the tunnelling barrier. This article extents the work of M. Parikh to GH black hole and HS black hole. Applying WKB approximation, we calculate the rate of Hawking radiation and found that the rate of tunnelling equals precisely the exponent of the difference of the entropy of the black hole before and after emission. We also obtain the result that the energy spectrum of radiation deviates from the exact thermality.

Big extra dimensions make lambda too small

I argue that the true quantum gravity scale cannot be much larger than the Planck length, because if it were then the quantum gravity-induced fluctuations in L would be insufficient to produce the observed cosmic "dark energy". If one accepts this argument, it rules out scenarios of the "large extra dimensions" type. I also point out that the relation between the lower and higher dimensional gravitational constants in a Kaluza-Klein theory is precisely what is needed in order that a black hole's entropy admit a consistent higher dimensional interpretation in terms of an underlying spatio-temporal discreteness.

Quantum Entropy of Black Hole with Internal Global Monopole

Using the generalized uncertainty relation, the new equation of statedensity is obtained, and then the entropy of black hole with an internalglobal monopole is discussed. The divergence that appears in black holeentropy calculation through original brick-wall model is overcome. Theresult of the direct proportion between black hole entropy and its eventhorizon area is drawn and given. The result shows that the black holeentropy must be the entropy of quantum state near the event horizon.

UNCERTAINTY RELATION AND BLACK HOLE ENTROPY OF TOROIDAL SPACETIME

By using the method of quantum statistics and via the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we avoid the difficulty of solving wave equation, and directly derive the partition functions of bosonic and fermionic field in Toroidal black hole. Then we calculate the entropies of bosonic and fermionic field near the black hole horizon on the background of a black hole. In our result, the divergent logarithmic term and ultraviolet cutoff in the original brick-wall method by which the black hole entropy was derived no longer exist. It is shown that the entropy of the black hole is proportional to the area of the horizon. These results are similar to that in the black hole with horizon topology S2.