多极矩分析的教与学探讨

多极矩展开是一种重要的分析方法，由静态电磁场多极矩展开得到的电多极子和磁多极子是基础而重要的物理模型.多极矩展开表示方法、多极子模型与多极子以及电磁场相互作用是多极矩分析教学的核心内容.本文从上述三个方面展开探讨：给出静态电场和静态磁场的内部和外部多极展开；讨论多极矩展开的不同表示的关系；强调多极子是基于远源处电磁势对源进行的等效点源替代；最后，从受力与力矩方面考察电多极子和磁多极子与外电磁场的相互作用.     

用量子隧穿法研究带质量四极矩静态黑洞的Hawking辐射

对带质量四极矩的静态黑洞Hawking辐射的隧穿过程进行了简单直接的推导，得到了热谱.因推导过程应用了能量守恒定律，故真正的辐射不一定是纯热的.这一结果支持了这样一种观点：隧穿的辐射携带信息是可能的. 关键词： 黑洞 辐射 隧穿 能量守恒     

静磁外部球谐多极矩展开

本文讨论静磁球谐多极矩展开,包括静磁标势和静磁矢势的外部球谐多极矩展开.在磁矢势外部球谐多极矩分析中介绍了两种不同的方法,方法一基于磁标势外部球谐多极矩展开求惯用磁矢势外部球谐多极矩展开,方法二从电流对远源场点磁矢势场贡献出发借助德拜势直接求得静磁矢势外部球谐多极矩展开的惯用表示.     

广义不确定关系与黑洞附近的热力学量

利用广义不确定关系修正的态密度计算了一般球对称静态黑洞附近无质量共形不变标量场、中微子场、电磁场、无质量Rarita-Schwinger场和引力场的热力学量.结果表明，黑洞附近的热力学量不仅依赖于黑洞的特征，还依赖于粒子的自旋和最小距离的尺度. 关键词： 广义不确定关系 一般球对称静态黑洞 热力学量     

超亮X射线源与中等质量黑洞

超亮X射线源是在邻近星系中发现的一类特殊的辐射X射线的天体.它们类似银河系中的黑洞双星,但却具有更高的亮度,因此可能包含更高质量的黑洞.即所谓的中等质量黑洞.中等质量黑洞并不像恒星级质量黑洞一样,可以是大质量恒星演化未期核塌缩的产物,因此在天体物理中具有重要意义.文章描述了超亮X射线源的一些基本性质,综述了近年来对这些源多波段观测的重要结果,以及这些结果对这些天体本质的暗示.     

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     

匀加速直线运动的Kerr黑洞的特征曲面

研究了作匀加速直线运动的变质量Kerr黑洞的三类特征曲面，即事件视界、表观视界和类时极限面(无限红移面).指出在变质量(存在吸积或蒸发)情况下，这类黑洞的三类特征曲面不再重合. 关键词：     

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     

考虑Hawking蒸发对Schwarzschild时空反作用后的静态球对称度规

由于黑洞具有Hawking辐射，它对时空必有影响(所谓反作用).结合用热力学方法研究黑洞反作用问题所得结果.应用求解考虑辐射场存在时的半经典爱因斯坦场方程.得出考虑Hawking蒸发对Schwarzschild时空反作用后的静态球对称度规.由此所得一切物理结论都是自洽的. 关键词：     

SL(n,R)户田黑洞的隧穿效应

由于SL(n,R)户田黑洞具有很好的数学结构,是研究黑洞物理较为理想的场所.本文主要研究其黑洞的霍金辐射,以及相关信息丢失问题.为了简单,只考虑在四维静态球对称SL(n,R)户田黑洞下,通过计算静止质量为零的粒子在事件视界附近隧穿效应来研究霍金辐射.在粒子的隧穿过程中,利用能量守恒并考虑了隧穿粒子对背景时空的反作用.获得粒子通过事件视界的隧穿概率取决于粒子出射前后黑洞熵的变化,并在此基础上讨论了其信息丢失问题,在满足一定条件下,我们的结果与RN黑洞和施瓦茨黑洞的结果一致.     

Modular inclusion,the Hawking temperature,and quantum field theory in curved spacetime

A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.     

Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox

Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.     

Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner–Nordström black-hole spacetime

The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner–Nordström black-hole spacetime are studied analytically. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein–Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner–Nordström-black-hole-charged-massive-scalar-field system.     

High-energy collision of two black holes

We study the head-on collision of two highly boosted equal mass, nonrotating black holes. We determine the waveforms, radiated energies, and mode excitation in the center of mass frame for a variety of boosts. For the first time we are able to compare analytic calculations, black-hole perturbation theory, and strong field, nonlinear numerical calculations for this problem. Extrapolation of our results, which include velocities of up to 0.94c, indicate that in the ultrarelativistic regime about 14+/-3% of the energy is converted into gravitational waves. This gives rise to a luminosity of order 10_(-2)c_(5)/G, the largest known so far in a black-hole merger.     

Accurate evolutions of orbiting black-hole binaries without excision

We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations, when used with a "precollapsed" initial lapse, is nonsingular at the start of the evolution and remains nonsingular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the innermost stable circular orbit regime. We show fourth-order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.     

Gravitational self-force correction to the binding energy of compact binary systems

Using the first law of binary black-hole mechanics, we compute the binding energy E and total angular momentum J of two nonspinning compact objects moving on circular orbits with frequency Ω, at leading order beyond the test-particle approximation. By minimizing E(Ω) we recover the exact frequency shift of the Schwarzschild innermost stable circular orbit induced by the conservative piece of the gravitational self-force. Comparing our results for the coordinate-invariant relation E(J) to those recently obtained from numerical simulations of comparable-mass nonspinning black-hole binaries, we find a remarkably good agreement, even in the strong-field regime. Our findings confirm that the domain of validity of perturbative calculations may extend well beyond the extreme mass-ratio limit.     

Normal-mode analysis for scalar fields in BTZ black-hole background

We analyze the possibility of inequivalent boundary conditions for a scalar field propagating in the BTZ black-hole space-time. We find that for certain ranges of the black-hole parameters, the Klein–Gordon operator admits a one-parameter family of self-adjoint extensions. For this range, the BTZ space-time is not quantum mechanically complete. We suggest a physically motivated method for determining the spectra of the Klein–Gordon operator.     

Black-hole thermodynamics: Entropy, information and beyond

We review some recent advances in black-hole thermodynamics including statistical mechanical origins of black-hole entropy and its leading order corrections from the view points of various quantum gravity theories. We then examine the problem of information loss and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.     

Instability of black hole horizon with respect to electromagnetic excitations

Analyzing exact solutions of the Einstein–Maxwell equations in the Kerr–Schild formalism we show that black hole horizon is instable with respect to electromagnetic excitations. Contrary to perturbative smooth harmonic solutions, the exact solutions for electromagnetic excitations on the Kerr background are accompanied by singular beams which have very strong back reaction to metric and break the horizon, forming the holes which allow radiation to escape interior of black-hole. As a result, even the weak vacuum fluctuations break the horizon topologically, covering it by a set of fluctuating microholes. We conclude with a series of nontrivial consequences, one of which is that there is no information loss inside of black-hole.     

The phase transition between caged black holes and black strings

Black-hole uniqueness is known to fail in higher dimensions, and the multiplicity of black hole phases leads to phase transitions physics in General Relativity. The black-hole black-string transition is a prime realization of such a system and its phase diagram has been the subject of considerable study in the last few years. The most surprising results seem to be the appearance of critical dimensions where the qualitative behavior of the system changes, and a novel kind of topology change. Recently, a full phase diagram was determined numerically, confirming earlier predictions for a merger of the black-hole and black-string phases and giving very strong evidence that the end-state of the Gregory–Laflamme instability is a black hole (in the dimension range 5?D?13$5?D?13$). Here this progress is reviewed, illustrated with figures, put into a wider context, and the still open questions are listed.