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.     

Tunneling of Dirac Particles from a Double Myers-Perry Black Hole in?Five?Dimensions

Motivated by the fermions tunneling formalism of Kerner and Mann, we attempt to investigate quantum tunneling of Dirac particles from a five dimensions double Myers-Perry black hole, which describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter and both in the same plane. After introducing several appropriate Gamma matrixes for the covariant Dirac equation, we obtain the tunneling probability of Dirac particles from the double Myers-Perry black hole, which gives the expected emission temperature as the case of scalar particles that obtained by others.     

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.     

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek’s semiclassical tunneling method.     

Dirac Particles＇ Hawking Radiation from a Schwarzschild Black Hole

Considering energy conservation and the backreaction of particles to spacetime, we investigate the massless/massive Dirac particles＇ Hawking radiation from a Schwarzschild black hole, The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the results obtained before. It satisfies the underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas the improved Damour-Rufflni method is more concise and understandable,     

Tunneling of Charged and Magnetized Fermions from the Kerr-Newman-Ads Black Hole with Magnetic Charges

Tunneling of charged and magnetized Dirac particles from the Kerr-Newman-Ads black hole with magnetic charges is discussed in this paper. Owing to the electric and magnetic fields would couple with gravity field, we introduce the Dirac equation of charged and magnetized particles. Then by redefining the equivalent charge and gauge potential corresponding to the source with electric and magnetic charges, we discuss this tunneling once and obtain the same Hawking temperature. Both results show that the fermions tunneling formalism also come into existence in the charged and magnetized background space time.     

Asymmetry of Hawking Radiation of Dirac Particles in a Charged Vaidya–de Sitter Black Hole

The Hawking radiation of Dirac particles in a charged Vaidya–de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. It is shown that the Hawking radiation of Dirac particles does not exist for P₁, Q₂ components, but for P₂, Q₁ components it does. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles.     

Generalized Uncertainty Principle and the Quantum Entropy of Rotating Black Hole

The entropy of rotating Kerr-Newman-Kasuya black hole due to massive charged fields （bosons and fermions） is calculated by using the new equation of state density motivated by the generalized uncertainty relation. The result shows the entropy does not depend on the mass and the charge but the parameter A, the area A and the spin of the fields. Moreover, an improved approximation is provided to calculate the scalar entropy.     

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.     

Hawking Radiation of Charged and Magnetized Particles from the Kerr-Newman-Kasuya Black Hole via Covariant Anomaly

Hawking radiation of a particle with electric and magnetic charges from the Kerr-Newman-Kasuya black hole is discussed in the dragging coordinate frame via the anomaly cancellation method, initiated by Robinson and Wilczek. We redefine an equivalent charge of the charged and magnetized black hole by reconstructing the electromagnetic field tensor. We adopt the refined covariant anomaly cancellation method to determining the compensating fluxes of charge flow and energy momentum tensor, which are proved to precisely match with those of the 2-dimensional blackbody radiation at the Hawking temperature with an appropriate chemical potential.     

New Coordinates for the Evaporating Vaidya Black Hole

Drawbacks of the ingoing Eddington-Finkelstein coordinates in describing the quantum thermal properties of the evaporating Vaidya black hole are presented. A new coordinate system we proposed previously [Acta Phys. Sin. 46 （1997） 1273] is employed. In this new coordinate system, the thermal radiation temperature of the Vaidya black hole is discussed again with the back reaction method.     

Charged Particle Tunnels from the Slowly Varying Reissner-Nordstroem Black Hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we discuss the Hawking radiation of the slowly varying Reissner-NordstrSm black hole by considering the unfixed background spacetime and the selfgravitation interaction. The result shows that the tunnelling rate is related to both the variation of BekensteinHawking entropy and the radiation spectrum deviating from the purely thermal one. This is in agreement with Parikh and Wilczek＇s result. Then a new method to study Hawking radiation of the non-stationary black holes is presented.     

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.     

Comparison of Approaches to Quantum Gravitational Corrections on the Reissner-Nordstr?m-de Sitter Black Hole Tunneling Radiation

Although the tunneling approach is fully established for black hole radiation, much work has been done to support the extension of this approach to more general settings. In this letter the Parikh-Kraus-Wilczeck tunneling proposal of black hole tunneling radiation is considered. The Reissner-Nordstr?m-de Sitter black hole thermodynamics is studied according to the generalized uncertainty principle and the modified dispersion relation analysis. It is shown that entropy, temperature and the original Parikh-Kraus-Wilczek calculations of the black hole tunneling probability receive new corrections. The results are compared and it is shown that these two alternative approaches lead to the same results if one uses the suitable expansion coefficients.     

Charged Particle’s Tunneling in a Modified Reissner-Nordstrom Black Hole

In the tunneling framework of Hawking radiation, charged particle’s tunneling in the modified Reissner-Nordstrom black hole from gravity’s rainbow is investigated. To this end, following the Schwarzschild solution in gravity’s rainbow, the metric of the modified Reissner-Nordstrom black hole is given. In the tunneling process, the metric fluctuation is taken into account, due to not only the energy conservation and electric charge conservation, but also the spacetime quantum effects. The calculation shows out that the emission rate satisfies the first law of black hole thermodynamics and is consistent with an underlying unitary theory. In addition, it is found that the entropy of the modified black hole is different to the Benkestein-Hawking entropy and the quantum corrections of the entropy appears.     

Tunneling of Charged and Magnetized Fermions from the Reissner-Nordström Black Hole with Magnetic Charges

The Kerner-Mann fermions tunneling framework is extended to the spin particles with electric and magnetic charges in this paper. We rewrite the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge. We only consider the case that the ratio of the electric charge and magnetic charge of the emission is constant and equal to the source. The result shows that when the energy conservation together with the electric charge and magnetic charge conservations are taken into account in the dynamical background space time, the emission rate agrees with the underlying unitary theory and the actual radiation spectrum of charged and magnetized fermions also derivates from the pure thermal one.     

Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo–Newtonian Potential

The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detailedly.An optimal fourth-order force gradient symplectic method,as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations,is used to calculate fast Lyapunov indicators.In this way,dynamical structures are described,and parameter domains for causing chaos are found.     

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.     

Quantum Tunneling Radiation of Charged Massive Particle from Reissner-Nordström-NUT Spacetime

By extending the semi-classical quantum tunneling method, the tunneling radiation of the massive charged particle from a charged Reissner-Nordström-NUT black hole was investigated. Difference from the uncharged mass-less particle, the geodesics of the charged massive particle tunneling from the black hole is not light-like, but determined by the phase velocity. The result shows that the tunneling rate depends on the emitted particle’s energy, NUT parameter and electric charge, and takes the same functional form as uncharged particle. It also proves that the exact emission spectrum is not strictly pure thermal, but is consistent with the underlying unitary theory.     

Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.