静态球对称黑洞的热质点模型及辐射功率

利用静态球对称黑洞的热质点模型,研究了黑洞的热辐射规律,得到了当η取固有厚度时,对所有Schwarzschild黑洞,其辐射功率都相同,其视界处的辐射能通量与黑洞的质量的平方成反比,而距黑洞遥远的观察者所接收到的辐射能通量与观测者到黑洞的距离的平方成反比; Reissner-Nordstrm黑洞视界处的辐射能通量和辐射功率不仅与黑洞的质量有关,还与黑洞的电荷有关,而距黑洞遥远的观察者所接收到的辐射能通量,当截断的固有厚度η、黑洞的质量m和电荷Q取定后与观测者到黑洞之间的距离的 关键词： 静态球对称黑洞 热质点模型 辐射功率 辐射能通量     

Radiation Energy Flux and Radiation Power of Schwarzschild Black Hole

Applying the entropy density near the event horizon, we obtained the result that the radiation energy flux of the black hole is always proportional to the quartic of the temperature of its event horizon. That is to say, the thermal radiation of the black hole always satisfies the generalized Stefan–Boltzmann law. The derived generalized Stefan–Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient which is related to the black hole mass, the kinds of radiation particles and space–time metric near the event horizon. In this paper, we have put forward a thermal particle model in curved space–time. By this model, the result has been obtained that when the thin film thickness and the cut-off distance are both fixed, the radiation energy flux received by observer far away from the Schwarzschild black hole is proportional to the average radial effusion velocity of the radiation particles in the thin film, and inversely proportional to the square of the distance between the observer and the black hole.     

Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordström black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case M ²>Q ². This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Schwarzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit Q→0. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.     

Radiation energy flux of Dirac field of static spherically symmetric black holes

By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan--Boltzmann law. The derived generalised Stenfan--Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space--time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner--Nordstrõm black hole are derived, separately.     

动态黑洞的瞬时辐出度

选取超前爱丁顿坐标，采用统计的方法，计算出动态黑洞的瞬时辐出度.结果表明，动态黑洞的瞬时辐出度不仅与假定黑洞处于热力学平衡时的辐出度有关，还与黑洞的事件视界变化率、事件视界温度、事件视界附近的熵密度及黑洞的吸收和辐射系数有关.对于球对称动态黑洞，任一时刻黑洞的瞬时辐出度总是正比于黑洞事件视界温度的四次方. 关键词： 熵密度 事件视界温度 薄膜模型 瞬时辐出度     

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerate horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordström black holes in higher dimensions.     

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.     

球对称动态黑洞视界附近的瞬时辐射能通量及瞬时辐射功率

采用黑洞的薄膜模型和局域热平衡的假定,研究球对称动态黑洞视界附近的瞬时辐射能通量和瞬时辐射功率,得到了当截断距离η取定后,Vaidya黑洞视界附近标量场的瞬时辐射能通量与黑洞的质量和视界变化率有关,其瞬时辐射功率仅与黑洞的视界变化率有关.Vaidya-Bonner黑洞的瞬时辐射能通量和瞬时辐射功率与黑洞的质量、电荷和视界变化率有关.表明黑洞周围的引力场、电磁场以及视界的变化均对黑洞的热辐射产生影响.     

Quantum corrections to the entropy of charged rotating black holes

Hawking radiation from a black hole can be viewed as quantum tunneling of particles through the event horizon. Using this approach we provide a general framework for studying corrections to the entropy of black holes beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics, we study charged rotating black holes and explicitly work out the corrections to entropy and horizon area for the Kerr–Newman and charged rotating BTZ black holes. It is shown that the results for other geometries like the Schwarzschild, Reissner-Nordström and anti-de Sitter–Schwarzschild spacetimes follow easily.     

The thermal radiation from dynamic black holes

Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole is calculated. It is found that the instantaneous radiation energy density of black hole is always proportional to the quartic of the temperature of event horizon in the same direction. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant, and it becomes a dynamic coefficient that is related to the event horizon changing rate, space-time structure near event horizon and the radiation absorption coefficient of the black hole. It is shown that there should be an internal relation between the gravitational field around black hole and its thermal radiation. Supported by the Science Foundation of Heze University (Grant No. XY06WL01)     

静态球对称黑洞Dirac场的Stefan-Boltzmann定律

利用静态球对称黑洞Dirac场的统计熵，导出静态球对称黑洞的Stefan-Boltzmann定律，得 到黑洞的辐出度与视界温度的四次方成正比的结论.发现Stefan-Boltzmann常数不同于平直 时空的值，并且在不同时空度规中该常数有不同的值. 关键词： 黑洞 统计熵 薄层模型 辐出度     

Hawking Radiation of the Charged Particles via Tunneling from the (<Emphasis Type="Italic">n</Emphasis>+2)-Dimensional Topological Reissner-Nordström-de Sitter Black Hole

Extending Parikh-Wilczek’s semi-classical tunneling method, we discuss the Hawking radiation of the charged massive particles via tunneling from the cosmological horizon of (n+2)-dimensional Topological Reissner-Nordström-de Sitter black hole.The result shows that, when energy conservation and electric charge conservation are taken into account, the derived spectrum deviates from the pure thermal one, but satisfies the unitary theory, which provides a probability for the solution of the information loss paradox.     

Hawking Radiation of Black Hole in Einstein-Proca Theory

The Hawking radiation of black hole in Einstein-Proca theory is discussed in this paper. The Einstein-Proca black hole is more general than Reissner-Nordström black hole, because Proca field is massive vector field. We calculate several quantum perturbations in this spacetime, and obtain the Hawking radiation at the horizon in Einstein-Proca theory.     

On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

Hawking radiation due to photon and gravitino tunneling

Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking’s periodicity argument, the modified metric for the Schwarzschild black hole is given. This corrected version of the metric, up to ? order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.     

Perfect fluid and scalar field in the Reissner-Nordström metric

We describe the spherically symmetric steady-state accretion of perfect fluid in the Reissner-Nordström metric. We present analytic solutions for accretion of a fluid with linear equations of state and of the Chaplygin gas. We also show that under reasonable physical conditions, there is no steady-state accretion of a perfect fluid onto a Reissner-Nordström naked singularity. Instead, a static atmosphere of fluid is formed. We discuss a possibility of violation of the third law of black hole thermodynamics for a phantom fluid accretion.     

Black holes coupled to scalar fields in higher-dimensional Kaluza-Klein theory

We derive in this paper an exact spherically symmetric solution coupled to scalar fields inn-dimensional Kaluza-Klein theory. A seven-dimensional solution is shown as a special case of the general solution. The solution has two even horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer horizon is due to the scalar fields.     

Quantum Anomaly and Hawking Radiation of Charged and Magnetized Reissner-Nordström de Sitter Black Hole

The recent work of Robinson and Wilczek that Hawking radiation can be determined by the compensating fluxes is extended to the charged and magnetized Reissner-Nordström de Sitter black hole. We reconstruct the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. We construct the effect field theory between the event horizon and cosmological horizon to respectively determine the compensating fluxes from them, which are shown to exactly equal to those of Hawking radiation, by the covariant anomaly cancellation conditions.     

Marginally Trapped Tubes Generated from Nonlinear Scalar Field Initial Data

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal, spherically symmetric marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initial data is sufficiently small and decays like O(r^-\frac12){O(r^{-\frac{1}{2}})}, and the potential function V is nonnegative with bounded second derivative. This result can be loosely interpreted as a statement about the stability of ‘nice’ asymptotic behavior of marginally trapped tubes under certain small perturbations of Schwarzschild.