Brick Wall Model and the Spectrum of a Schwarzschild Black Hole

The quantum entropy of a scalar field near a Schwarzschild black hole is investigated by employing the brick-wall model in the grand canonical ensemble. A positive chemical potential is introduced if the cutoff is set to be of order of the Planck length. We also discuss the relation between the chemical potential and the mass quantum of the black hole.     

Black hole remnants due to GUP or quantum gravity?

Based on the micro-black hole gedanken experiment as well as on general considerations of quantum mechanics and gravity the generalized uncertainty principle (GUP) is analyzed by using the running Newton constant. The result is used to decide between the GUP and quantum gravitational effects as a possible mechanism leading to the black hole remnants of about Planck mass.     

Top quark production from black holes at the CERN LHC

LHC is expected to be a top quark factory. If the fundamental Planck scale is near a TeV, then we also expect the top quarks to be produced from black holes via Hawking radiation. In this Letter we calculate the cross sections for top quark production from black holes at the LHC and compare it with the direct top quark cross section via parton fusion processes at next-to-next-to-leading order (NNLO). We find that the top quark production from black holes can be larger or smaller than the pQCD predictions at NNLO depending upon the Planck mass and black hole mass. Hence the observation of very high rates for massive particle production (top quarks, Higgs or supersymmetry) at the LHC may be an useful signature for black hole production.     

Statistical-Mechanical Entropy of a Black Hole with a Global Monopole to All Orders in Planck Length

Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle, we calculate the statistical entropy of the scalar field in the global monopole black hole spacetime without any artificial cutoff. It is shown that the entropy is proportional to the horizon area.     

Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss

Using standard statistical method, we discover the existence of correlations among Hawking radiations (of tunneled particles) from a black hole. The information carried by such correlations is quantified by mutual information between sequential emissions. Through a careful counting of the entropy taken out by the emitted particles, we show that the black hole radiation as tunneling is an entropy conservation process. While information is leaked out through the radiation, the total entropy is conserved. Thus, we conclude the black hole evaporation process is unitary.     

Black hole quantum tunnelling and black hole entropy correction

The Parikh–Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated once more in this work. The first order correction, the log-corrected entropy-area relation, emerges naturally in the tunnelling picture if we consider the emission of a spherical shell. The second order correction to the emission rate for the Schwarzschild black hole is also calculated. At this level, the entropy of the black hole will contain three parts: the usual Bekenstein–Hawking entropy, a logarithmic term and an inverse area term. We find that the coefficient of the logarithmic term is −1. Thus, apart from a coefficient, our correction to the black hole entropy is consistent with that calculated in loop quantum gravity.     

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.     

Quantum black hole and the modified uncertainty principle

Recently Ali et al. (2009) [13] proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Planck length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number n which coincides with Bekenstein?s proposal. We also found that the mass of the black hole is directly proportional to the quantum number n when quantum gravity effects are taken into consideration via the modified uncertainty relation but it reduces the value of mass for a particular value of the quantum number.     

Strong chaos of fast scrambling yields order: Emergence of decoupled quantum information capsules

The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold atoms in a pure entangled state. We provide a QIC speculation of black hole evaporation.     

Exact solutions for shells collapsing towards a pre-existing black hole

The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well-known “frozen star” paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this Letter. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no “frozen star” is formed for an external observer as matter falls towards a black hole. Therefore, we predict that only gravitational wave radiation can be produced in the final stage of the merging process of two coalescing black holes. Our results also indicate that for the clock of an external observer, matter, after crossing the event horizon, will never arrive at the “singularity” (i.e. the exact center of the black hole), i.e., for all black holes with finite lifetimes their masses are distributed within their event horizons, rather than concentrated at their centers. We also present a worked-out example of the Hawking's area theorem.     

Axionic black holes and wormholes

Theories in which gravity is coupled to a Kalb-Ramond field are known to have black hole solutions characterized by the value of the conserved axion charge. The Kalb-Ramond field configuration for these black holes has vanishing field strength. The axion charge may be measured by an analog of the Aharanov-Bohm interference effect. The axion-charge to mass ratio may be arbitrarily large, as contrasted to the case of the Reissner-Nordstrom black hole where the electric-charge to mass ratio has an upper bound of one. The generic endpoint of semiclassical evaporation of an axionic black hole would therefore be an object of very large axion charge with mass of order the Planck mass. Axion charge also couples to Giddings-Strominger type instantons (wormholes) present in these theories. Instead of evaporating completely, therefore, it is likely that an axionic black hole will be swallowed by a wormhole, avoiding the appearance of a naked singularity. The loss of quantum coherence is a more subtle issue.This essay received the third award from the Gravity Research Foundation for the year 1989-Ed.On leave from the Physics Department, Syracuse University, Syracuse NY 13244-1130, USA.     

Corrected Hawking Tunneling Radiation in the Higher Dimensional Reissner-Nordström Black Hole

Based on the generalized uncertainty principle, in which the quantum gravitational effects are properly taken in to account, the corrected Bekenstein-Hawking entropy of the higher dimensional Reissner-Nordström black hole, up to the square order of Planck length, has been calculated. Using the corrected entropy, the black hole radiation probability has been calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and a generalized quantum tunneling through the event horizon of the black hole is obtained.     

Black holes and large N species solution to the hierarchy problem

We provide the perturbative and non‐perturbative arguments showing that theories with large number of species of the quantum fields, imply an inevitable hierarchy between the masses of the species and the Planck scale, shedding a different light on the hierarchy problem. In particular, using the black hole physics, we prove that any consistent theory that includes N Z₂‐conserved species of the quantum fields of mass Λ, must have a value of the Planck mass, which in large N limit is given by M_P² \gsim N Λ². An useful byproduct of this proof is that any exactly conserved quantum charge, not associated with a long‐range classical field, must be defined maximum modulo N, with N \gsim (M_P/m)², where m is the mass of the unit charge. For example, a continuous global U(1) ‘baryon number’ symmetry, must be explicitly broken by gravity, at least down to a Z_N subgroup, with N \lsim (M_P/m_b)², where m_b is the baryon mass. The same constraint applies to any discrete gauge symmetry, as well as to other quantum‐mechanically‐detectable black hole charges that are associated with the massive quantum hair of the black hole. We show that the gravitationally‐coupled N‐species sector that solves the gauge hirearchy problem, should be probed by LHC.     

Universality of black hole quantum computing

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.     

Regular black holes in UV self-complete quantum gravity

In this Letter we investigate the role of regular (curvature singularity-free) black holes in the framework of UV self-complete quantum gravity. The existence of a minimal length, shielding the trans-Planckian regime to any physical probe, is self-consistently included into the black hole probe itself. In this way we obtain to slightly shift the barrier below the Planck length, with the UV self-complete scenario self-consistently confirmed.     

Hawking temperature of Kerr–Newman–AdS black hole from tunneling

Using the null-geodesic tunneling method of Parikh and Wilczek, we derive the Hawking temperature of a general four-dimensional rotating black hole. In order to eliminate the motion of ? degree of freedom of a tunneling particle, we have chosen a reference system that is co-rotating with the black hole horizon. Then we give the explicit result for the Hawking temperature of the Kerr–Newman–AdS black hole from the tunneling approach.     

Canonical Entropy and Phase Transition of Rotating Black Hole

Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Havcking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.     

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.     

Black hole entropy,log correction and inverse area correction

In this Letter, we first extend the Parikh–Wilczek tunneling framework to a general spherically symmetric black hole, and calculate the tunneling rate of the emission particles to the second order accuracy. Then, by assuming the emission process satisfies an underlying unitary theory, we correct the entropy of a general spherically symmetric black hole. We find that the log correction and the inverse area correction to the entropy is also suitable for a general spherically symmetric black hole.     

Will black holes eventually engulf the Universe?

The Babichev–Dokuchaev–Eroshenko model for the accretion of dark energy onto black holes has been extended to deal with black holes with non-static metrics. The possibility that for an asymptotic observer a black hole with large mass will rapidly increase and eventually engulf the Universe at a finite time in the future has been studied by using reasonable values for astronomical parameters. It is concluded that such a phenomenon is forbidden for all black holes in quintessential cosmological models.