Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.     

Quantum geometry and entanglement entropy of a black hole

We have studied here black hole entropy in the framework of quantum geometry. It is pointed out that the black hole radiation consistent with Hawking spectrum can be realized as an effect of quantum geometry using a dynamical formalism for diffeomorphism invariance which envisages a discretized unit of time in the Planck scale. This formalism suggests that torsion acts within a quantized area unit (area bit) associated with a loop and this eventually forbids the Hamiltonian constraint to be satisfied for a finite loop size. We assign a spin with torsion in each area bit and entanglement entropy of a black hole is computed in terms of the entanglement entropy of this spin system. We have derived the Bekenstein-Hawking entropy along with a logarithmic correction term with a specific coefficient. Also we have shown that the Bekenstein-Hawking entropy can be formulated in terms of the Noether charge associated with a diffeomorphism invariant Lagrangian.     

On the effect of the degeneracy among dark energy parameters

A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle’s energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.     

Quantum Black Hole

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early universe, in the quantum cosmology scenario the black hole is essentially created from nothing. The black hole originates from a constrained gravitational instanton. The probability of creation for all kinds of single black holes in the Kerr-Newman family, at the semiclassical level, is the exponential of the total entropy of the universe, or one quarter of the sum of both the black hole and the cosmological horizon areas. The de Sitter spacetime is the most probable evolution at the Planckian era.     

Quantum hair and quantum gravity

A black hole may carry quantum numbers that arenot associated with massless gauge fields, contrary to the spirit of the no-hair theorems. The quantum hair is invisible in the classical limit, but measurable via quantum interference experiments. Quantum hair alters the temperature of the radiation emitted by a black hole. It also induces non-zero expectation values for fields outside the event horizon; these expectation values are non-perturbative in , and decay exponentially far from the hole. The existence of quantum hair demonstrates that a black hole can have an intricate quantum-mechanical structure that is completely missed by standard semiclassical theory.Based on an essay which received second award from the Gravity Research Foundation, 1991     

Holography and Non-Locality in a Closed Vacuum-Dominated Universe

A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the maximum number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta in the universe cause quantum transitions in the wavefunction specifying the distribution of mass throughout the universe, with instantaneous non-local effects throughout the universe.     

Black hole and holographic dark energy

We discuss the connection between black hole and holographic dark energy. We examine the issue of the equation of state (EOS) for holographic energy density as a candidate for the dark energy carefully. This is closely related to the EOS for black hole, because the holographic dark energy comes from the black hole energy density. In order to derive the EOS of a black hole, we may use its dual (quantum) systems. Finally, a regular black hole without the singularity is introduced to describe an accelerating universe inside the cosmological horizon. Inspired by this, we show that the holographic energy density with the cosmological horizon as the IR cutoff leads to the dark energy-dominated universe with ωΛ=−1${\omega }_{\Lambda }=-1$.     

Spectrum of a quantized black hole,correspondence principle,and holographic bound

An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either does not comply with the holographic bound or requires a special choice of the Barbero-Immirzi parameter for the horizon surface, distinct from its value for other quantized surfaces. The problem of distinguishability of the edges in LQG is discussed, with the following conclusion: Only under the assumption of partial distinguishability of the edges can the microcanonical entropy of a black hole be made both proportional to the horizon area and satisfying the holographic bound.     

Can an astrophysical black hole have a topologically non-trivial event horizon?

In 4-dimensional General Relativity, there are several theorems restricting the topology of the event horizon of a black hole. In the stationary case, black holes must have a spherical horizon, while a toroidal spatial topology is allowed only for a short time. In this Letter, we consider spinning black holes inspired by Loop Quantum Gravity and by alternative theories of gravity. We show that the spatial topology of the event horizon of these objects changes when the spin parameter exceeds a critical value and we argue that the phenomenon may be quite common for non-Kerr black holes. Such a possibility may be relevant in astrophysics, as in some models the accretion process can induce the topology transition of the horizon.     

The large numbers hypothesis and quantum mechanics

In this paper, the suggested similarity between micro and macrocosmos is extended to quantum behavior, postulating that quantum mechanics, like general relativity and classical electrodynamics, is invariant under discrete scale transformations. This hypothesis leads to a large scale quantization of angular momenta. Using the scale factor Λ ~ 10³⁸, the corresponding quantum of action, obtained by scaling the Planck constant, is close to the Kerr limit for the spin of the universe - when this is considered as a huge rotating black hole - and to the spin of Gödel’s universe, solution of Einstein equations of gravitation. Besides, we suggest the existence of another, intermediate, scale invariance, with scale factor λ ~ 10¹⁹. With this factor we obtain, from Fermi’s scale, the values for the gravitational radius and for the collapse proper time of a typical black hole, besides the Kerr limit value for its spin. It is shown that the mass-spin relations implied by the two referred scale transformations are in accordance with Muradian’s Regge-like relations for galaxy clusters and stars. Impressive results are derived when we use a λ-scaled quantum approach to calculate the mean radii of planetary orbits in solar system. Finally, a possible explanation for the observed quantization of galactic redshifts is suggested, based on the large scale quantization conjecture.     

In Favor of a Newtonian Quantum Gravity

We list arguments for creating a unified theory of Newtonian Gravity and Quantum Mechanics. This nonrelativistic level has been historically bypassed, however even here one is confronted with conceptional problems anticipating some features of Relativistic Quantum Gravity. Bearing in mind Wigner's famous analysis on measurabilitity in the relativistic case here a genuine uncertainty of the Newton potential is verified, leading to the breakdown of the Schrödinger equation when leaving microscopic regions.     

Quantum aspects of black hole entropy

This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly.     

Letter: Quantum Nonthermal Radiation of Nonstationary Kerr-Newman-de Sitter Black Holes

Quantum nonthermal radiation of a nonstationary Kerr-Newman-de Sitter black hole is investigated. A crossing of the positive and negative Dirac energy levels occurs in a region near the event horizon of the hole, and spontaneous quantum nonthermal radiation takes place in the overlap region.     

Gibbons-Maeda dilaton黑洞的全息熵

依据全息原理,通过计算Gibbons-Maeda dilaton黑洞事件视界上量子场的统计熵,得到了该黑洞的全息熵和Bekenstein-Hawking熵.计算中利用非对易量子场论,克服了普通量子场论中态密度在视界上的发散困难,避免了黑洞熵热气体方法中紫外截断的引入.用留数定理克服了计算中的积分困难,所得的结果定量成立.研究表明,黑洞熵可以视为其视界上量子场的熵;通过计算视界上量子态的统计熵可以得到黑洞熵,计算中可以且应该避免视界外量子态的影响. 关键词： 黑洞熵 全息原理 事件视界 非对易量子场论     

量子史瓦茨黑洞和暗物质

引入Sommerfeld作用量量子化条件来处理Schwarzschild黑洞的量子化问题. 发现此类量子化黑洞存在一个质量为m_G=123m_p的基态，处于基态的量子Schwarzschild黑洞不再存在Hawking蒸发和任何其他辐射，可名之曰暗星. 它的存在不仅可以解决信息丢失的疑难，而且极可能是构成暗物质的主要候选者. 关键词： 量子史瓦茨黑洞 暗物质     

Holographic Entropy Bound of a Nonstationary Black Hole

In accordance with the holographic principle, by counting the states of the scalar field just at the event horizon of the Vaidya-Bonner black hole, the holographic entropy bound of the black hole is calculated and the Bekenstein- Hawking formula is obtained, With the generalized uncertainty principle, the divergence of state density at event horizon in the ordinary quantum field theory is removed, With the residue theorem, the integral trouble in the calculation is overcome. The present result is quantitatively tenable and the holographic principle is realized by applying the quantum field theory to the black hole entropy problem. Compared with some previous works, it is suggested that the quantum states contributing to black hole entropy should be restricted on the event horizon.     

Review: Gas of Wormholes: A Possible Ground State of Quantum Gravity

In order to gain insight into the possible Ground State of Quantized Einstein's Gravity, we have derived a variational calculation of the energy of the quantum gravitational field in an open space, as measured by an asymptotic observer living in an asymptotically flat space-time. We find that for Quantum Gravity (QG) it is energetically favourable to perform its quantum fluctuations not upon flat space-time but around a "gas" of wormholes of mass m _p, the Planck mass (m _p 10¹⁹ GeV) and average distance l _p, the Planck length a _p(a _p 10^–33 cm). As a result, assuming such configuration to be a good approximation to the true Ground State of Quantum Gravity, space-time, the arena of physical reality, turns out to be well described by Wheeler's quantum foam and adequately modeled by a space-time lattice with lattice constant l _p, the Planck lattice.