Tunneling of Charged Massive Particles from Taub-NUT-Reissner-Nordström-AdS Black Holes

We apply the null-geodesic method to investigate tunneling radiation of charged and magnetized massive particles from Taub-NUT-Reissner-Nordström black holes endowed with electric as well as magnetic charges in Anti-de Sitter (AdS) spaces. The geodesics of charged massive particle tunneling from the black hole is not lightlike, but can be determined by the phase velocity. We find that the tunneling rate is related to the difference of Bekenstein-Hawking entropies of the black hole before and after the emission of particles. The entropy differs from just a quarter area at the horizon of black holes with NUT parameter. The emission spectrum is not precisely thermal anymore and the deviation from the precisely thermal spectrum can bring some information out, which can be treated as an explanation to the information loss paradox. The result can also be treated as a quantum-corrected radiation temperature, which is dependent on the black hole background and the radiation particle’s energy and charges.     

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.     

Tunneling Radiation of Charged and Magnetized Particles from the Reissner-Nordstr?m-de Sitter Black Holes with Magnetic Charges

We extended the Parikh-Wilczek’s method to calculate the tunneling radiation of charged and magnetized particles from the event horizon and the cosmological horizon of the Reissner-Nordstr?m-de Sitter black hole with magnetic charges. We reconstructed the electromagnetic field tensor and recalculated the Lagrangian of the field corresponding to the source with electric and magnetic charges. By viewing the eclectic and magnetic charges as an equivalent electric charge, we obtained the tunneling rate of the charged and magnetized particles. Our calculation supports the conclusion given by Parikh and Wilczek that the emission spectrum is no longer purely thermal, and the emission process supports the information conservation.     

Charged Particles’ Hawking Radiation via Tunneling of Both Horizons from Reissner-Nordström-Taub-NUT Black Holes

In some recent derivations thermal characters of the inner horizon have been employed; however, the understanding of possible role that may play the inner horizons of black holes in black hole thermodynamics is still somewhat incomplete. Motivated by this problem we investigate Hawking radiation of the Reissner-Nordström-Taub-NUT (RNTN) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour-Ruffini method and the thin film brick wall model to calculate the temperature and the entropy of the inner horizon of the RNTN black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area, and it thus may contribute to the total entropy of the black hole in the context of Nernst theorem. Considering conservations of energy and charge and the back-reaction of emitting particles to the spacetime, the emission spectra are obtained for both the inner and outer horizons. The total emission rate is the product of the emission rates of the inner and outer horizons, and it deviates from the purely thermal spectrum and can bring some information out. Thus, the result can be treated as an explanation to the information loss paradox.     

Virtual Black Holes and Space–Time Structure

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought.     

Tunnelling Radiation of Charged and Magnetized Massive Particles from BTZ Black Holes

We investigate the tunnelling radiation of charged and magnetized massive particles from a Banados-Teitelboim- Zanelli （BTZ） black hole by extending the Parikh-Wilczek tunnelling framework. In order to calculate the emission rate, we reconstruct the electromagnetic field tensor and the Lagrangia~n of the field corresponding to the source with electric and magnetic charges, and treat the charges as an equivalent electric charge for simplicity in the later calculation. The result supports Parikh-Wilczek＇s conclusion, that is, the Hawking thermal radiation actually deviates from perfect thermality and agrees with an underlying unitary theory.     

Thermodynamics of Black Holes in Einstein-Maxwell-Gauss-Bonnet Theory

We study the black hole solution in Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity theory with a cosmological constant in five dimension. It is a generalization of the Reissner-Nordström-de Sitter (RNdS) or RNAdS (Reissner-Nordström-Anti-de Sitter) black hole solutions (according as the cosmological constant is positive or negative) in the Einstein-Gauss-Bonnet (EGB) theory. We analyze the thermodynamic quantities of EMGB black hole and find a restriction involving the charge and the cosmological constant for the existence of an extremal black hole. Finally, Hawking-Page phase transition has been discussed for the present black hole.     

Quasinormal Modes of Clifton–Barrow Black Holes

In this paper, we study the theoretical quasinormal modes produced by scalar perturbations around a static, spherically symmetric black hole with exterior metric described by the Clifton–Barrow solution of R ^1+δ gravity. It is found that the δ-correction increases both the real and imaginary part of the quasinormal frequency. Compared with those of ordinary Schwarzschild black hole with the same size, the oscillating quasi-period of scalar perturbation of Clifton–Barrow black hole is remarkably short for the case of low multi-pole quantum number l, while the difference of the damping time scales is slight. However, in the large l limit, the relative differences of both real and imaginary part of quasinormal modes have the same amplitude.     

Entropy of Einstein—Maxwell-Dilaton—Axion Black Holes

The entropy of Einstein—Maxwell-dilaton—axion black holes is calculated by using the improved brick-wall model. Taking into account of the statistical physics, we propose not to consider the superradiant modes. The result shows that the nonsuperradiant modes do contribute exactly the area-law entropy for extreme black hole. Moreover, our cut-off which does not require an angular cut-off is independent of angle . As for the extreme black hole, we found that its entropy is zero.     

Object Picture of Quasinormal Modes for Stringy Black Holes

We study the quasinormal modes （QNMs） for stringy black holes. By using numerical calculation, the relations between the QNMs and the parameters of black holes are minutely shown. For （1＋1）-dimensional stringy black hole, the real part of the quasinormal frequency increases and the imaginary part of the quasinormal frequency decreases as the mass of the black hole increases. Furthermore, the dependence of the QNMs on the charge of the black hole and the flatness parameter is also illustrated. For （1＋3）-dimensional stringy black hole, increasing either the event horizon or the multipole index, the real part of the quasinormal frequency decreases. The imaginary part of the quasinormal frequency increases no matter whether the event horizon is increased or the multipole index is decreased.     

Brick Walls for Nonstationary Black Holes

The validity condition of the brick-wall model is analysed in nonstationary space-time.It is shown that the model holds only in thin regions,only by using tortoise coordinates near the event horizon of a slowly varying(quasistationary)black hole.The reason for the use of tortoise cooridnates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time.Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.     

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.     

Effect of Spin on Thermodynamical Quantities around Reissner-Nordstroem Black Holes

Using the quantization procedure involving in the Boulware vacuum state and Killing time t, we evaluate the entropy density, energy density, pressure and equation of state around the Reissner-Nordstroem black hole by the Wentzel-Kramers-Brillouin approximation on the Teukolsky-type master equation. We find that, near the event horizon, there exist subleading order terms with spin dependence beyond the expected Minkowskian hightemperature contribution. In particular, the terms are important and cannot be neglected for near-extremal black hole cases. At large r, the Boulware state approaches the Minkowski vacuum and the theory agrees with that performed in Minkowski spacetime.     

Inner Structure of Entropy of Reissner–Nordström Black Holes

Using the relationship between the entropy and the Euler characteristic, and the usual decomposition of spin connection, an entropy density is introduced to describe the inner structure of the entropy of RN black holes. It is pointed out that the entropy of RN black holes is determined by the singularities of the timelike Killing vector field of RN spacetime, and that these singularities carry the topological numbers, Hopf indices and Brouwer degrees, naturally, which are topological invariants. Taking account of the physical meaning of entropy in statistics, the entropy and its density of RN black holes are modified and they are given by the Hopf indices merely.     

Charged Dirac Particles’ Hawking Radiation via Tunneling of Both Horizons and Thermodynamics Properties of Kerr–Newman–Kasuya–Taub–NUT–AdS Black Holes

We investigate Hawking radiation of electrically and magnetically charged Dirac particles from a dyonic Kerr–Newman–Kasuya–Taub–NUT–Anti-de Sitter (KNKTN–AdS) black hole by considering thermal characters of both the outer and inner horizons. We apply Damour–Ruffini method and membrane method to calculate the temperature and the entropy of the inner horizon of the KNKTN–AdS black hole. The inner horizon admits thermal character with positive temperature and entropy proportional to its area. The inner horizon entropy contributes to the total entropy of the black hole in the context of Nernst theorem. Considering conservation of energy, charges, angular momentum, and the back-reaction of emitting particles to the spacetime, we obtain the emission spectra for both the inner and outer horizons. The total emission rate is obtained as the product of the emission rates of the inner and outer horizons. It deviates from the purely thermal spectrum with the leading term exactly the Boltzman factor and can bring some information out. The result thus can be treated as an explanation to the information loss paradox.     

Calabi–Yau Black Holes and (0,4) Sigma Models

When an M-theory fivebrane wraps a holomorphic surface › in a Calabi-Yau 3-fold X the low energy dynamics is that of a black string in 5 dimensional — =1 supergravity. The infrared dynamics on the string worldsheet is an — = (0,4) 2D conformal field theory. Assuming the 2D CFT can be described as a nonlinear sigma model, we describe the target space geometry of this model in terms of the data of X and ›. Variations of weight two Hodge structures enter the construction of the model in an interesting way.     

Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe?

The discovery of a large number of supermassive black holes (SMBH) at redshifts , when the Universe was only 900 million years old, raises the question of how such massive compact objects could form in a cosmologically short time interval. Each of the standard scenarios proposed, involving rapid accretion of seed black holes or black hole mergers, faces severe theoretical difficulties in explaining the short‐time formation of supermassive objects. In this work we propose an alternative scenario for the formation of SMBH in the early Universe, in which energy transfer from superconducting cosmic strings piercing small seed black holes is the main physical process leading to rapid mass increase. As a toy model, the accretion rate of a seed black hole pierced by two antipodal strings carrying constant current is considered. Using an effective action approach, which phenomenologically incorporates a large class of superconducting string models, we estimate the minimum current required to form SMBH with masses of order by . This corresponds to the mass of the central black hole powering the quasar ULAS J112001.48+064124.3 and is taken as a test case scenario for early‐epoch SMBH formation. For GUT scale strings, the required fractional increase in the string energy density, due to the presence of the current, is of order 10⁻⁷, so that their existence remains consistent with current observational bounds on the string tension. In addition, we consider an “exotic” scenario, in which an SMBH is generated when a small seed black hole is pierced by a higher‐dimensional string, predicted by string theory. We find that both topological defect strings and fundamental strings are able to carry currents large enough to generate early‐epoch SMBH via our proposed mechanism.     

Quantum Tunneling of Massive Particles from a Garfinkle-Horowitz-Strominger Dilatonic Black Hole

Hawking radiation is viewed as a process of quantum tunneling. The massive particles＇ tunneling from Garfinkle-I-Iorowitz-Strominger black hole is investigated. Using Jingyi Zhang＇s de Broglie wave method, we get the unthermal spectrum, and the result is consistent with the underlying unitary theory.