Quantum Gravity Corrections to the Tunneling Radiation of Scalar Particles

The original derivation of Hawking radiation shows the complete evaporation of black holes. However, theories of quantum gravity predict the existence of the minimal observable length. In this paper, we investigate the tunneling radiation of the scalar particles by introducing the quantum gravity effects influenced by the generalized uncertainty principle. The Hawking temperatures are not only determined by the properties of the black holes, but also affected by the quantum numbers of the emitted particles. The quantum gravity corrections slow down the increase of the temperatures. The remnants are found during the evaporation.     

The ringing of quantum corrected Schwarzschild black hole with GUP

Schwarzschild black holes with quantum corrections are studied under scalar field perturbations and electromagnetic field perturbations to analyze the effect of the correction term on the potential function and quasinormal mode (QNM). In classical general relativity, spacetime is continuous and there is no existence of the so-called minimal length. The introduction of the correction items of the generalized uncertainty principle, the parameter β, can change the singularity structure of the black hole gauge and may lead to discretization in time and space. We apply the sixth-order WKB method to approximate the QNM of Schwarzschild black holes with quantum corrections and perform numerical analysis to derive the results of the method. Also, we find that the effective potential and QNM in scalar fields are larger than those in electromagnetic fields.     

The uncertainty principle and Bekenstein–Hawking entropy corrections

There is much attention on the corrections to Bekenstein–Hawking entropy in area with a model-dependent coefficient. The corrections are generally composed of two parts: quantum corrections and thermal corrections. The generalized uncertainty principle (GUP), which will reduce to the conventional Heisenberg relation in situations of weak gravity, is one of the candidates to be utilized to obtain the quantum corrections to the Bekenstein–Hawking entropy. Recently the extended uncertainty principle (EUP) and generalized extended uncertainty principle (GEUP) are introduced to calculate entropy corrections with large length scales limit. In this paper, we obtain the quantum corrections to Bekenstein–Hawking entropy in four-dimensional Schwarzschild black holes based on the EUP and GEUP. Some attractive results are derived.     

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.     

Black Hole Entropies of the Thin Film Model and the Membrane Model Without Cutoffs

Taking into account the effect of the generalized uncertainty principle on the generalized black hole entropy and tacking the thin film brick-wall model, we calculate the entropy of the quantum scalar field in generalized static black hole. The Bekenstein–Hawking entropies of all well-known static black holes are obtained. The entropy of 2-D membrane just at the event horizon of static black hole is also calculated, and the result of the black hole entropy proportional to the event horizon area can be obtained more easily and generally. This discussion shows that black hole entropy is just identified with the entropy of the quantum field on the event horizon. The difference from the original brick-wall model is that the present result is convergent without any cutoff and the little mass approximation is removed. With residue theorem, the integral difficulty in the calculation of black hole entropy is overcome.     

Entropy of Four-Dimensional Spherically Symmetric Black Holes with Planck Length

Considering corrections to all orders in Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the Bose field and Fermi field on the background of the four-dimensional spherically symmetric black holes without any cutoff. It is obtained that the statistical entropy is directly proportional to the area of horizon.     

Information entropy for static spherically symmetric black holes

By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein--Hawking entropy when the suitable cutoff factor is adopted.     

Entropy of the rotating and charged black string to all orders in the Planck length

<正>By using the entanglement entropy method,this paper calculates the statistical entropy of the Bose and Fermi fields in thin films,and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string.Here,the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string.Taking into account the effect of the generalized uncertainty principle on quantum state density,it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model.These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect.The ultraviolet cut-off in the brick-wall model is not reasonable.The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics,the correction value of Bekenstein-Hawking entropy is obtained.This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.     

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.     

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.     

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.     

Direct imaging rapidly-rotating non-Kerr black holes

Recently, two of us have argued that non-Kerr black holes in gravity theories different from General Relativity may have a topologically non-trivial event horizon. More precisely, the spatial topology of the horizon of non-rotating and slow-rotating objects would be a 2-sphere, like in Kerr space–time, while it would change above a critical value of the spin parameter. When the topology of the horizon changes, the black hole central singularity shows up. The accretion process from a thin disk can potentially overspin these black holes and induce the topology transition, violating the Weak Cosmic Censorship Conjecture. If the astrophysical black hole candidates are not the black holes predicted by General Relativity, we might have the quite unique opportunity to see their central region, where classical physics breaks down and quantum gravity effects should appear. Even if the quantum gravity region turned out to be extremely small, at the level of the Planck scale, the size of its apparent image would be finite and potentially observable with future facilities.     

Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.     

Quantum correction to the entropy of noncommutative BTZ black hole

In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes. We also show that the area entropy product of the noncommutative BTZ black holes is dependent on mass and by analyzing the nature of the specific heat capacity we have observed that the noncommutative BTZ black hole is stable at some range of parameters.     

Black hole mass threshold from nonsingular quantum gravitational collapse

Quantum gravity is expected to remove the classical singularity that arises as the end state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous scalar field. We show that nonperturbative semiclassical effects of loop quantum gravity cause a bounce and remove the black hole singularity. Furthermore, we find a critical threshold scale below which no horizon forms: quantum gravity may exclude very small astrophysical black holes.     

Measuring the Last Burst of Non-singular Black Holes

Non-perturbative quantum gravity prevents the formation of curvature singularities and may allow black holes to decay with a lifetime shorter than evaporation time. This, in connection with the existence of primordial black holes, could open a new window for quantum-gravity phenomenology. I discuss the possibility of observing astrophysical emissions from the explosion of old black holes in the radio and in the gamma wavelengths. These emissions can be discriminated from other astrophysical sources because of a peculiar way the emitted wavelength scales with the distance. The spectrum of the diffuse radiation produced by those objects presents a peculiar distortion due to this scaling.     

Hiding Information in Theories Beyond Quantum Mechanics,and It’s Application to the Black Hole Information Problem

The black hole information problem provides important clues for trying to piece together a quantum theory of gravity. Discussions on this topic have generally assumed that in a consistent theory of gravity and quantum mechanics, quantum theory is unmodified. In this review, we discuss the black hole information problem in the context of generalisations of quantum theory. In this preliminary exploration, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We are able to calculate the time it takes information to escape a black hole, assuming that information is preserved. In quantum mechanics, information should escape pure state black holes after half the Hawking photons have been emitted, but we find that this get’s modified in generalisations of quantum mechanics. Likewise the black-hole mirror result of Hayden and Preskill, that information from entangled black holes can escape quickly, also get’s modified. We find that although information exits the black hole as predicted by quantum theory, it is fairly generic that it fails to appear outside the black hole at this point—something impossible in quantum theory due to the no-hiding theorem. The information is neither inside the black hole, nor outside it, but is delocalised.     

Tunnelling from black holes and tunnelling into white holes

Hawking radiation is nowadays being understood as tunnelling through black hole horizons. Here, the extension of the Hamilton–Jacobi approach to tunnelling for non-rotating and rotating black holes in different non-singular coordinate systems not only confirms this quantum emission from black holes but also reveals the new phenomenon of absorption into white holes by quantum mechanical tunnelling. The rôle of a boundary condition of total absorption or emission is also clarified.