Area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes from quasinormal modes

The area spectra of extreme Kerr and nearly extreme Kerr–Newmann black holes are investigated from quasinormal modes via Maggiore’s physical interpretation of quasinormal modes. Using the first law of black hole thermodynamics and the action variable quantization, we arrive at consistent equally spaced area and entropy spectra. Results show that the spectra are irrelevant to the parameters of the black holes and the perturbation fields, which fully agree with Bekensteins original conjecture. In the calculations, we have defined the corresponding Hawking temperatures of the black holes following the suggestion of Mäkelä et al. to avoid the zero temperature and to guarantee the (nearly-) extreme black holes quantizable.     

The dangers of extremes

While extreme black hole spacetimes with smooth horizons are known at the level of mathematics, we argue that the horizons of physical extreme black holes are effectively singular. Test particles encounter a singularity the moment they cross the horizon, and only objects with significant back-reaction can fall across a smooth (now non-extreme) horizon. As a result, classical interior solutions for extreme black holes are theoretical fictions that need not be reproduced by any quantum mechanical model. This observation suggests that significant quantum effects might be visible outside extreme or nearly extreme black holes. It also suggests that the microphysics of such black holes may be very different from that of their Schwarzschild cousins.     

Quantum Statistical Entropy of Six Dimensional Horowitz-Strominger Black Holes

Using the membrane model which is developed from the brick-wall model, we calculated the bosonic and fermionic entropy of 6-d Horowitz-Strominger black holes. The result shows the quantum entropy of such black holes is still proportional to the area of the event horizon only if the cut-off is properly chosen. As for the extreme black holes,the entropy approaches zero.     

Geometric Character of Black-Hole Entropy

The geometry of the neighborhood near an event horizon is similar to the Rindlermetric, which leads to the thermal effect of black holes. The entropy of the scalarfield and the Dirac field are calculated in the black-hole background. The entropyof the scalar field, which is proportional to the area of the event horizon, isnaturally derived. Under the condition of large-mass black hole, the entropy ofthe Dirac field is still proportional to the area of the horizon. These results canbe applied to a large class of black holes. A new method for calculating the blackhole entropy is proposed which makes it easy to calculate the entropy of ahigh-spin field in the black-hole background. We also consider extreme black holesand point out that the topological entropy only has classical meaning.     

极端黑洞的熵和拓扑

文章作者提出,自然界中存在两种拓扑性质完全不同的极端黑,一种是Hawking提出的具体有极端拓扑的极端黑洞,它的熵是零;另一种极端黑洞保留了非极端黑洞的拓扑,它的熵仍然可用Bekenstein-Hawking公式描述,文章的结论解决了近年来极端黑洞研究中Hawking学派和弦理论家之间的矛盾,解决了Hawking党派观点和黑洞相变理论的矛盾。     

Supermembranes on black holes

We report a new family of supermembrane vacua possesing the Siegel symmetry. This family consists of bosonic solutions of supermembrane field equations and describes static, toroidal membranes in d=11 black hole spacetimes. The black holes we consider are obtained by embedding the d=4 Reissner-Nordström solutions into d=11, N=1 supergravity. We show that supermembranes pick, as their backgrounds, only the extreme Reissner-Nordström black holes and require the d=4 magnetic charge to be non-zero. Moreover, the membranes on dyonic holes can be interpreted, at the linearized level, as fluctuations of the membranes on magnetically charged holes. The quantisation around the toroidal membranes on the magnetically charged, extreme black holes therefore poses itself as an interesting problem.     

Geometry and Entropy of Two Kinds of Extreme Kerr-Newmann Black Holes

Geometric and thermodynamical properties of two kinds of extreme Kerr-Newmann black holes have been investigated. We find that different values of entropy appear for these two kinds of extreme black holes and these results have close relation to their geometry.     

静态球对称黑洞的热质点模型及辐射功率

利用静态球对称黑洞的热质点模型,研究了黑洞的热辐射规律,得到了当η取固有厚度时,对所有Schwarzschild黑洞,其辐射功率都相同,其视界处的辐射能通量与黑洞的质量的平方成反比,而距黑洞遥远的观察者所接收到的辐射能通量与观测者到黑洞的距离的平方成反比; Reissner-Nordstrm黑洞视界处的辐射能通量和辐射功率不仅与黑洞的质量有关,还与黑洞的电荷有关,而距黑洞遥远的观察者所接收到的辐射能通量,当截断的固有厚度η、黑洞的质量m和电荷Q取定后与观测者到黑洞之间的距离的 关键词： 静态球对称黑洞 热质点模型 辐射功率 辐射能通量     

Area and entropy spectra of black holes via an adiabatic invariant

By considering and using an adiabatic invariant for black holes, the area and entropy spectra of static spherically-symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.     

Fragile black holes

The AdS/CFT correspondence may give a new way of understanding field theories in extreme conditions, as in the quark–gluon plasma phase of quark matter. The correspondence normally involves asymptotically AdS black holes with dual field theories which are defined on locally flat boundary spacetimes; the implicit assumption is that the distortions of spacetime which occur under extreme conditions do not affect the field theory in any unexpected way. However, AdS black holes are [to varying degrees] fragile, in the sense that they become unstable to stringy effects when their event horizons are sufficiently distorted. This implies that field theories on curved backgrounds may likewise be unstable in a suitable sense. We investigate this phenomenon, focussing on the “fragility” of AdS₅ black holes with flat event horizons. We find that, when they are distorted, these black holes are always unstable in string theory. This may have consequences for the detailed structure of the quark matter phase diagram at extreme values of the spacetime curvature.     

Area Spectra of d-Dimensional Extreme Reissner-Nordström Black Holes

With the physical interpretation of quasinormal modes proposed by Maggiore, we investigate the quantum area and entropy spectra of d-dimensional extreme Reissner-Nordström black holes. Employing two methods, the method of Maggiore and the action variable quantization, we arrive at the spectra consistent with each other. Results show that the spectra are irrelevant to the black hole parameters and the perturbation field parameters but relative to the spacetime dimension. For a given dimension, the spectra are equally spaced.     

Topological Aspects of Entropy and Phase Transition of Kerr Black Holest

In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem, it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime. By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4 for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.     

Topological Aspects of Entropy and Phase Transition of Kerr Black Holes

In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem,it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime.By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.     

Thermal statistical ensembles of classical extreme black holes

New statistical ensembles of classical extreme black holes are introduced. Each ensemble is proven to represent a non extreme, finite temperature black hole. This mean or average black hole is surrounded by a mean electromagnetic field and a so-called apparent matter, which is the large scale trace of the averaged upon small scale fluctuations of the gravitational and electromagnetic fields. However, the total mass and the total charge of space-time is not modified by the averaging.     

Astrophysical Black Holes: A Compact Pedagogical Review

Black holes are among the most extreme objects that can be found in the Universe and an ideal laboratory for testing fundamental physics. Here, the basic properties of black holes as expected from general relativity, the main astronomical observations, and the leading astrophysical techniques to probe the strong gravity region of these objects are reviewed. The main intention is to provide a compact introductory overview on astrophysical black holes to new students entering this research field, as well as to senior researchers working in general relativity and alternative theories of gravity, who wish to quickly learn the state of the art of astronomical observations of black holes.     

黑洞与奇点

黑洞可以说是引力最极端的体现,其视界内是个连光也逃不出去的时空区域。近来黑洞在天 文观测方面取得令人惊讶的发展,这其中包括：黑洞碰撞的引力波探测以及M87 星系的超大质量 黑洞的所谓第一张黑洞照片。但是在理论的层面上,黑洞物理尚有许多未解之谜。其中,信息遗失 的悖论是最有名的。但是,有另一个问题至少和信息的丢失一样{甚至更加{令人费解的,就是黑洞 内部的奇点性质。时空奇点是广义相对论本身无法描述的,在那里究竟发生什么事？黑洞内部的奇 点和宇宙大爆炸时的奇点有何不同？奇点是否会裸露在黑洞外面？所谓“宇宙监督猜想”的假设目 前有何进展？我们在这篇半科普的文章中简单的介绍这些课题,希望本文章对物理和数学的本科生 有所帮助。     

Area spectrum of slowly rotating black holes

We investigate the area spectrum for rotating black holes which are Kerr and BTZ black holes. For slowly rotating black holes, we use the Maggiore's idea combined with Kunstatter's method to derive their area spectra, which are equally spaced.     

Novel CFT duals for extreme black holes

In this paper, we study the CFT duals for extreme black holes in the stretched horizon formalism. We consider the extremal RN, Kerr-Newman-AdS-dS, as well as the higher dimensional Kerr-AdS-dS black holes. In all these cases, we reproduce the well-established CFT duals. Actually we show that for stationary extreme black holes, the stretched horizon formalism always gives rise to the same dual CFT pictures as the ones suggested by ASG of corresponding near horizon geometries. Furthermore, we propose new CFT duals for 4D Kerr-Newman-AdS-dS and higher dimensional Kerr-AdS-dS black holes. We find that every dual CFT is defined with respect to a rotation in certain angular direction, along which the translation defines a U(1) Killing symmetry. In the presence of two sets of U(1) symmetry, the novel CFT duals are generated by the modular group SL(2,Z), and for n sets of U(1) symmetry there are general CFT duals generated by T-duality group SL(n,Z).     

Different Quantum Entropies for Two Kinds of Extreme Two-Dimensional Lowe-Strominger Black Holes

It is shown that both the classical entropy of two-dimensional extremal LoweStrominger black hole and the quantum entropy of the scalar field in the background of this black hole are different by using Hawking's treatment as wel as Zaslavskii's treatment respectively. This result supports our previous suggestion that there are two kinds of extreme black holes in the nature. A new divergent term emerges in the quantum entropy in Zaslavskii's treatment and its physical meaning has been discussed.