Entropy Of Kerr Black Hole Research Articles

Fast scrambling of mutual information in Kerr-AdS5

We compute the disruption of mutual information in a TFD state dual to a Kerr black hole with equal angular momenta in AdS5 due to an equatorial shockwave. The shockwave respects the axi-symmetry of the Kerr geometry with specific angular momenta {mathcal{L}}_{phi_1} & {mathcal{L}}_{phi_2} . The sub-systems considered are hemispheres in the left and the right dual CFTs with the equator of the S3 as their boundary. We compute the change in the mutual information by determining the growth of the HRT surface at late times. We find that at late times leading up to the scrambling time the minimum value of the instantaneous Lyapunov index {lambda}_L^{left(min right)} is bounded by kappa =frac{2pi {T}_H}{left(1-mu {mathcal{L}}_{+}right)} and is found to be greater than 2πTH in certain regimes with TH and μ denoting the black hole’s temperature and the horizon angular velocity respectively while {mathcal{L}}_{+} = {mathcal{L}}_{phi_1} + {mathcal{L}}_{phi_2} . We also find that for non-extremal geometries the null perturbation obeys {mathcal{L}}_{+} < μ−1 for it to reach the outer horizon from the AdS boundary. The scrambling time at very late times is given by κτ* ≈ log mathcal{S} where mathcal{S} is the Kerr entropy. We also find that the onset of scrambling is delayed due to a term proportional to log(1 − {mu mathcal{L}}_{+} )−1 which is not extensive and does not scale with the entropy of Kerr black hole.

Bubbling the NHEK

We build the first family of smooth bubbling microstate geometries that are asymptotic to the near-horizon region of extremal five-dimensional Kerr black holes (NHEK). These black holes arise as extremal non-supersymmetric highly-rotating D1-D5- P solutions in type IIB string theory on T4×S1. Our solutions are asymptotically NHEK in the UV and end in the IR with a smooth cap. In the context of the Kerr/CFT correspondence, these bubbling geometries are dual to pure states of the 1+1 dimensional chiral conformal field theory dual to NHEK. Since our solutions have a bubbling structure in the IR, they correspond to an IR phase of broken conformal symmetry, and their existence supports the possibility that all the pure states whose counting gives the Kerr black hole entropy correspond to horizonless bulk configurations.

The influence of the generalized uncertainty principle on Kerr black hole thermodynamics

The quantum corrections on Kerr black hole thermodynamics was studied by using the generalized uncertainty principle. Based on the quantum uncertainty of the particle near the event horizon, the relation between the temperature and the radius of the rotating black hole was given. Then, by analyzing the relation formula, the critical state and the critical parameters of the black hole were obtained. Further, with the help of the first law of black hole thermodynamics, the thermal capacity and the entropy of Kerr black hole were calculated. And, according to the obtained thermal capacity formula, the radiation remnant of Kerr black hole was given. It was found that, the remnant state of the rotating black hole was consistent with the critical state. Such, for Kerr black hole, the temperature singularity during evaporation can be avoided by the generalized uncertainty principle. In addition, the obtained black hole entropy contained the quantum corrected terms and the logarithmic correction was proved.

Extended symmetries at the black hole horizon

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.

Kerr Black Hole Entropy and its Quantization

By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.

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.

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.

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.

Generalized Uncertainty Principle and Correction Value to the Kerr Black Hole Entropy

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking black hole entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the correction value of the black hole entropy by utilizing the generalized uncertainty principle and obtain the correction term caused by the generalized uncertainty principle. Because in our calculation we think that the Bekenstein-Hawking area theorem is still valid after considering the generalized uncertainty principle, we derive that the coefficient of the logarithmic term of the black hole entropy correction term is positive. This result is different from the known result at present. Our method is valid not only for single horizon spacetime but also for spin axial symmetric spacetimes with double horizons. In the whole process, the physics idea is clear and calculation is simple. It offers a new way for studying the entropy correction of the complicated spacetime.

SEMICLASSICAL (QFT) AND QUANTUM (STRING) ROTATING BLACK HOLES AND THEIR EVAPORATION: NEW RESULTS

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature Ts at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M &gt; m Pl , angular momentum J and charge Q is a string state of temperature Ts, string mass Ms, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α′c), a new phase transition at a temperature [Formula: see text], higher than Ts. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S sem (M, J), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For M ≫ m Pl and J &lt; GM2/c, [Formula: see text] is the leading term, but for high angular momentum, (nearly extremal case J = GM2/c), a gravitational phase transition operates and the whole entropy S sem is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. This new extremal black hole transition occurs at a temperature T sem J = (J/ℏ)T sem , higher than the Hawking temperature T sem .

Entropy Correction for Kerr Black Hole**The projectsupported by National Natural Science Foundationof China under Grant No. 10374075 and the NaturalScience Foundation of Shanxi Province of China under Grant No. 2001009

In this paper, we discuss leading-order correctionsto the entropy of Kerr black hole due to thermal fluctuations inthe finite cavity. Then temperature is constant, the solutionof the black hole is obtained within a cavity, that is, the solutionof the spacetime after considering the radiation of the blackhole. Therefore, we derive that the location of the black holehorizon and specific heat are the functions of temperature andthe radius of the cavity. Corrections to entropy also are relatedto the radius of the cavity. Through calculation, we obtain conditionsof taking the value of the cavity's radius. We provide a newway for studying the corrections of complicated spacetimes.

Topological Aspects of Entropy and Phase Transition ofKerr Black Holes**The project supported by the Natural Science Foundation ofShanghai Municipal Commission of Science and Technology underGrant Nos. 04ZR14059 and 04DZ05905, National Natural Science Foundation ofChina under Grant No. 10447125

In the light of topological current and the relationship betweenthe entropy and the Euler characteristic, thetopological aspects of entropy and phase transition of Kerr blackholes are studied. From Gauss–Bonnet–Chern theorem, it isshown that the entropy of Kerr black holes is determined by thesingularities of the Killing vector field of spacetime. Bycalculating the Hopf indices and Brouwer degrees of the Killingvector field at the singularities, the entropy S = A/4 fornonextreme Kerr black holes and S = 0 for extreme ones areobtained, respectively. It is also discussed that, with the changeof the ratio of mass to angular momentum for unit mass, the Eulercharacteristic and the entropy of Kerr black holes will changediscontinuously when the singularities on Cauchy horizon mergewith the singularities on event horizon, which will lead to thefirst-order phase transition of Kerr black holes.

Intrinsic topological structure of entropy of Kerr black holes

In the light of φ-mapping method and the relationship between entropy and the Euler characteristic, the intrinsic topological structure of entropy of Kerr black holes is studied. From the Gauss-Bonnet-Chem theorem, it is shown that the entropy of Kerr black hole is determined by singularities of the Killing vector field of spacetime. These singularities naturally carry topological numbers, Hopf indices and Brouwer degrees, which can also be viewed as topological quantization of entropy of Kerr black holes. Specific results S=A/4 for non-extreme Kerr black holes and S=0 for extreme ones are calculated independently by using the bove-mentioned methods.

U(N)-MONOPOLES ON KERR BLACK HOLE AND ITS ENTROPY

We describe U(N)-monopoles (N&gt;1) on Kerr black holes using the parameters of the moduli space of holomorphic vector U(N)-bundles over [Formula: see text] with the help of the Grothendieck splitting theorem. For N = 2,3 we obtain this description in an explicit form as well as the estimates for the corresponding monopole masses. This gives us a possibility to adduce some reasonings in favor of the existence of both a fine structure for Kerr black holes and the statistical ensemble tied with it which might generate the Kerr black hole entropy.