Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Analytic solutions in the dyon black hole with a cosmic string: Scalar fields,Hawking radiation and energy flux

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.     

Hawking Temperature Calculation Using Tunneling Mechanism

Based on the black hole tunneling mechanism in which the ingoing particles should be absorbed absolutely, Hamilton-Jacobi method is modified to investigate Hawking radiation from a Schwarzschild black hole once again. The results are independent on the coordinates and the standard Hawking temperature is obtained without the factor of 2 problem. Moreover, it is also pointed out that the modified Hamilton-Jacobi method can be applied to investigate Hawking radiation from the general horizons in dynamical spacetimes.     

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity.The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions.We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.     

视界和温度格林函数的生成泛函

在平衡态条件下,利用格林函数的欧氏生成泛函讨论了具有视界的Rindler时空和黑洞时空中量子场温度的几何来源。在Minkowski时空到Rindler时空的变换下,绝对零度格林函数欧氏生成泛函的路径积分表示变换为有限温度量子场的相应表示,说明Minkowski真空态和Rindler时空中的一量子混合态性质相同,导出了这个态的温度格林函数及各热力学格林函数。对于Schwarzschild,Reissner-Nordstrom和Kerr黑洞,得到了类似的结果,并获得了描写量子混合态的统计算符的具体形式。 关键词：     

黑洞的统计熵

运用量子统计的方法,直接求解Schwarzschild时空背景下玻色场和费米场的配分函数,得到熵的积分表达式.按照最近的研究结果,认为黑洞的Hawking辐射过程是隧道效应过程,在考虑黑洞隧道效应产生过程中黑洞能量发生变化的基础上,给出积分的下限为黑洞的视界位置.由此得到黑洞熵的主要项为视界面积的1/4.不存在使人疑惑的紫外截断因子,并且由此可得黑洞辐射粒子的能量与辐射温度成正比的结论. 关键词： 黑洞熵 量子统计 隧道效应 反作用     

洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

Fermions Tunnelling with Quantum Gravity Correction

Based on the generalized uncertainty principle (GUP), we investigate the correction of quantum gravity to Hawking radiation of black hole by utilizing the tunnelling method. The result tells us that the quantum gravity correction retards the evaporation of black hole. Using the corrected covariant Dirac equation in curved spacetime, we study the tunnelling process of fermions in Schwarzschild spacetime and obtain the corrected Hawking temperature. It turns out that the correction depends not only on the mass of black hole but also on the mass of emitted fermions. In our calculation, the quantum gravity correction slows down the increase of Hawking temperature during the radiation explicitly. This correction leads to the remnants of black hole and avoids the evaporation singularity.     

Greybody factor for a scalar field coupling to Einstein's tensor

We study the greybody factor and Hawking radiation for a scalar field coupling to Einstein's tensor in the background of Reissner–Nordström black hole in the low-energy approximation. We find that the presence of the coupling terms modifies the standard results in the greybody factor and Hawking radiation. Our results show that both the absorption probability and Hawking radiation increase with the coupling constant. Moreover, we also find that for the stronger coupling, the charge of black hole enhances the absorption probability and Hawking radiation of the scalar field, which is different from those of ones without coupling to Einstein's tensor in the black hole spacetime.     

Schwarzschild-de Sitter黑洞的Hawking辐射

利用延拓Damour-Ruffini方法,研究Schwarzschild-de Sitter黑洞的Hawking辐射.在保持时空中总能量守恒的条件下,考虑辐射粒子对时空的反作用和黑洞事件视界与宇宙视界的相互关联后,得到黑洞辐射谱.此辐射不再是严格的纯热谱,与黑洞事件视界和宇宙视界对应Bekenstein-Hawking熵变有关,发现其结果仍然符合幺正性原理. 关键词： Damour-Ruffini方法 Hawking辐射 能量守恒     

Pseudo-Newtonian potentials and the radiation emitted by a source swirling around a stellar object

We use pseudo-Newtonian potentials to compute the scalar radiation emitted by a source orbiting a stellar object. We compare the results obtained in this approach with the ones obtained via quantum field theory in Schwarzschild spacetime. We find that, up to the marginally stable circular orbit, the potential that better reproduces the Schwarzschild results is the Nowak–Wagoner one. For unstable circular orbits, none of the pseudo-Newtonian potentials considered in our analysis produces satisfactory results. We show that the Paczyński–Wiita potential, the most used in the literature to analyze accretion disks, generates the least satisfactory results for the scalar radiation emitted by the source in circular orbit around a Schwarzschild black hole.     

Hawking radiation and page curves of the black holes in thermal environment

As realistic objects in the Universe, the black holes are surrounded by complex environment. By taking the effect of thermal environment into account, we investigate the evaporation process and the time evolutions (page curves) of the entanglement entropies of Hawking radiation of various types of black holes. It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation. For Schwarzschild black hole and Reissner-Nordström black hole in flat spaces, when the initial temperature of the black hole is higher than the environment temperature, the black holes evaporate completely and the Hawking radiation is eventually purified. For Schwarzschild-AdS black hole, it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature. Otherwise, it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole. Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.     

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.     

HORIZONS AND GENERATING FUNCTIONALS FOR THE TEMPERATURE GREEN FUNCTIONS

The generating functional approach to Green functions in the thermal equilibrium is used to explore the geometrical origin of the temperatures of the quantum fields in the Rindler space-time and black hole spacetimes. It is shown that under the transformation from Minkowski space to the Rindler space the path integral representation for the Euclidean generating functionals of Green functions at zero temperature would transform into the corresponding ones of the quantum fields at a certain finite temperature, and the Minkowski vacuum state would have the same properties as that of the quantum mixed state at the same temperatfire. All thermal Green functions for the mixed state are given. Similar results would be obtained for the Schwarzschild, the Reissner-NordstrOm and the Kerr black holes and whereupon the Hawking temperature for the black holes would have geometrical origin as well as that in the Rindler spacetime. The various density operators of the mixed states at the Hawking temperature for the black hole sacetimes are specified.     

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.     

A simpler method for researching fermions tunneling from black holes

A new simpler mathematic method is proposed to study fermions tunneling from black holes. According to this method, by using semiclassical approximation theory, it simplifies the Dirac equation of curved spacetime and then the relationship of the gamma matrix and the component of contravariant metric is considered in order to transform the set of difficult quantum equations into a simple equation. Finally, the fermion tunneling and Hawking radiation of black holes are obtained. The method is very effective and simple, and we will take the Schwarzschild black hole with global monopole and the higher-dimensional Reissner-Nordstrom de Sitter black hole as two examples to show the fact.     

Late-time Evolution of the Yang-Mills Field in the Spherically Symmetric Gravitational Collapse

We investigate the late-time evolution of theYang-Mills field in the self-gravitating backgrounds:Schwarzschild and Reissner-Nordstrom spacetimes. Thelate-time power-law tails develop in the threeasymptotic regions: the future timelike infinity, thefuture null infinity and the black hole horizon. Inthese two backgrounds, however, the late-time evolutionhas quantitative and qualitative differences. In the Schwarzschild black hole background, thelate-time tails of the Yang-Mills field are the same asthose of the neutral massless scalar field withmultipole moment l = 1. The late-time evolutionis dominated by the spacetime curvature. When the backgroundis the Reissner-Nordstrom black hole, the late-timetails have not only a smaller power-law exponent, butalso an oscillatory factor. The late-time evolution is dominated by the self-interacting term ofthe Yang-Mills field. The cause responsible for thedifferences is revealed.     

Hawking Temperature of a Static Black Hole in Harmonic Coordinates

Hawking radiation is usually studied in standard coordinates. In this paper, we calculate the Hawking temperature of a Schwarzschild black hole in harmonic coordinates, as well as that of a Reissner-Nordström black hole. The action of a scalar field near the event horizon can be formulated exactly without omitting some high-order terms. We show dimensional reduction for Hawking temperature is also valid for harmonic coordinates, and verify further that the results are independent on concrete coordinates. With the help of Lorentz transformation, our work might also serve as a basis to investigate the thermal radiation from a moving black hole.