Cosmological Black Holes

In this paper we propose a model for the formation of the cosmological voids. We show that cosmological voids can form directly after the collapse of extremely large wavelength perturbations into low-density black holes or cosmological black holes (CBH). Consequently the voids are formed by the comoving expansion of the matter that surrounds the collapsed perturbation. It follows that the universe evolves, in first approximation, according to the Einstein-Straus cosmological model. We discuss finally the possibility to detect the presence of these black holes through their weak and strong lensing effects and their influence on the cosmic background radiation.     

Black Holes as Atoms

Stationary spacetimes containing a black hole have several properties akin to those of atoms. For instance, such spacetimes have only three classical degrees of freedom, or observables, which may be taken to be the mass, the angular momentum, and the electric charge of the hole. There are several arguments supporting a proposal originally made by Bekenstein that quantization of these classical degrees of freedom gives an equal spacing for the horizon area spectrum of black holes. We review some of these arguments and introduce a specific Hamiltonian quantum theory of black holes. Our Hamiltonian quantum theory gives, among other things, a discrete spectrum for the classical observables, and it produces an area spectrum which is closely related to Bekenstein's proposal. We also present a foamlike model of horizons of spacetime. In our model spacetime horizon consists of microscopic Schwarzschild black holes. Applying our Hamiltonian approach to this model we find that the entropy of any horizon is one quarter of its area.     

Black Holes and Inflation

A model for black hole collapse and evaporation in which the black hole is supposed to be an excited state of one of the Planck black holes pervading the structure of spacetime is discussed. By assuming a Coleman-Weinberg gravitational effective potential for a scalar field inside the collapse matter, it is shown that the black hole state cannot be attained neither through bubble tunneling nor by the rolling down of the field.     

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。     

Noncommutative Singular Black Holes

In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact （t - r） dependence of solution in terms of the noncommutative parameter σ. In this setup, there Js no black hole remnant at long times.     

Noncommutative Singular Black Holes

In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact (t - r) dependence of solution in terms of the noncommutative parameter σ. In this setup, there is no black hole remnant at long times.     

On Naked Black Holes

The recently proposed criteria for naked blackholes are conveniently rephrased. It is shown that twosolutions of dilaton-Maxwell gravity, satisfying weakenergy conditions, represent naked blackholes.     

Black Holes Are One-Dimensional

The holographic principle has revealed that phyical systems in 3-D space, black holes included, are basically two-dimensional as far as their information content is concerned. This conclusion is complemented by one sketched here: as far as entropy or information flow is concerned, a black hole behaves as a one-dimensional channel. We define a channel in flat spacetime in thermodynamic terms, and contrast it with common entropy emitting systems. A black hole is more like the former: its entropy output is related to the emitted power as it would be for a one-dimensional channel, and disposal of an information stream down a black hole is limited by the power invested in the same way as for a one-dimensional channel.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Black Holes in Accelerated Universe

We have analyzed the evolution of mass of a stationary black hole in the standard FRW cosmological model. The evolution is determined specifically about the time of transition from the earlier matter to the later exotic dark energy dominated universe. It turns out that the accretion rate of matter on the black hole of mass was approximately O(10²⁰) higher than the accretion rate of exotic dark energy at the time of transition.     

Black Holes Without Spacelike Singularities

It is shown that for small, spherically symmetric perturbations of asymptotically flat two-ended Reissner–Nordström data for the Einstein–Maxwell-real scalar field system, the boundary of the dynamic spacetime which evolves is globally represented by a bifurcate null hypersurface across which the metric extends continuously. Under additional assumptions, it is shown that the Hawking mass blows up identically along this bifurcate null hypersurface, and thus the metric cannot be extended twice differentiably; in fact, it cannot be extended in a weaker sense characterized at the level of the Christoffel symbols. The proof combines estimates obtained in previous work with an elementary Cauchy stability argument. There are no restrictions on the size of the support of the scalar field, and the result applies to both the future and past boundary of spacetime. In particular, it follows that for an open set in the moduli space of solutions around Reissner–Nordström, there is no spacelike component of either the future or the past singularity.     

Gravitational Waves and Black Holes

In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than formalism. Dynamical solutions representing traveling waves as well as stationary fields like those of black holes are discussed. Their properties are investigated by studying the geodesic structure of the corresponding space-times, as representing the motion of point-like test particles. The interaction between gravitational, electro-magnetic and scalar fields is also considered.     

Spectroscopies of Extreme Black Holes

The spectroscopies of extreme black holes are investigated by the intrinsic property of these black holes in this paper. We find that the area spectrum of the extreme Reissner-Nordstrom black hole is dependent on the fine structure constant. While the area spectra share the same expression and are determined by the quantum numbers of angular momentum for the extreme Kerr-Sen Dilaton-Axion and Kaluza-Klein black holes.     

Myerse-Perry Black Holes with Logarithmic Correction

In this paper we consider Myers-Perry black holes and study thermodynamics and statistics under logarithmic correction of the entropy. We calculate effect of logarithmic correction of thermodynamics quantities such as entropy. We study thermodynamics stability of the model by using the specific heat. We claim that the correction term removes some instabilities and matches statistical entropy with BH entropy.     

Corrected Entropy of BTZ Black Holes

In this paper, corrected entropy of a class of BTZ black holes, include charge and rotation, studied. We obtain corrected Bekenstein-Hawking entropy and find that effect of charge viewed at order A ^?2, and effect of rotation viewed at order A ^?6, therefore Q and J don’t have contribution in corrected entropy lower than the second order. We also write the first law of black hole thermodynamics for the case of charged rotating BTZ black hole.     

Regular Black Holes with Cosmological Constant

We present a class of regular black holes with cosmological constant Λ in nonlinear electrodynamics. Instead of usual singularity behind black hole horizon, all fields and curvature invariants are regular everywhere for the regular black holes. Through gauge invariant approach, the linearly dynamical stability of the regular black hole is studied. In odd-parity sector, we find that the Λ term does not appear in the master equations of perturbations, which shows that the regular black hole is stable under odd-parity perturbations. On the other hand, for the even-parity sector, the master equations are more complicated than the case without the cosmological constant. We obtain the sufficient conditions for stability of the regular black hole. We also investigate the thermodynamic properties of the regular black hole, and find that those thermodynamic quantities do not satisfy the differential form of first law of black hole thermodynamics. The reason for violating the first law is revealed.     

Discrete Spectra of Charged Black Holes

Bekenstein proposed that the spectrum of horizon area of quantized black holes must be discrete and uniformly spaced. We examine this proposal in the context of spherically symmetric charged black holes in a general class of gravity theories. By imposing suitable boundary conditions on the reduced phase space of the theory to incorporate the thermodynamic properties of these black holes and then performing a simplifying canonical transformation, we are able to quantize the system exactly. The resulting spectra of horizon area, as well as that of charge are indeed discrete. Within this quantization scheme, near-extremal black holes (of any mass) turn out to be highly quantum objects, whereas extremal black holes do not appear in the spectrum, a result that is consistent with the postulated third law of black hole thermodynamics.