Entropy of a rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein-Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.

Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-Flat SdS Black String Space with Polynomial Approximation

As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzsehild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.

Entropy Quantization from a Neutral Black String

Taking into account the Bekenstein-Hawking area law,based on the analysis of Zeng and Liu et al.that area spectrum is determined by the periodicity of an outgoing wave,we discuss on the quantization of entropy from a neutral black string.In addition,applying the adiabatic invariant quantity method proposed by Majhi and Vagenas,we further verify the entropy quantum of the neutral black string.As a result,two different methods show that the quantum of entropy is △S = 2π,which is in agreement with Bekenstein's proposal.

A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources

It is explicitly shown how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at r=0due to a non-vanishing scalar curvature involving the Dirac delta distribution. In order to achieve this, one is required to extend the domain of r to negative values −∞≤r≤+∞. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin r=0which furnish the Schwarzschild black hole entropy in all dimensions D≥4after evaluating the Euclidean Einstein-Hilbert action. Two of the most salient results are i) that the observed spacetime dimension D=4is precisely singled out from all the other dimensions when the strong and weak energy conditions are met, and ii) the point mass source described in this work is not the result of a spherically symmetric gravitational collapse of a star as described by the Oppenheimer-Snyder model because we are not neglecting the pressure. As usual, it is required to take the inverse Hawking temperature βHas the length of the circle Sβ1obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation, it=τ, to imaginary time. This approach can be generalized to the Reissner-Nordstrom and Kerr-Newman metrics. The physical implications of this finding warrant further investigation since it suggests a profound connection between the notion of gravitational entropy and spacetime singularities.

Charged Randall-Sundrum Braneworld Type Ⅱ with Higher Order Curvature Corrections from Superstring Arguments and Dominated by Quintessence

We discuss a new class of RSII braneworld cosmology exhibiting accelerated expansion and dominated by quintessence. It is explicitly demonstrated that the universe expansion history （transition from inflation to deceleration epoch to acceleration and effective quintessence era） may naturally occur in such unified theory for some classes of inverse scalar potentials. Besides a decaying effective cosmological constant, the model incorporates an increasing black hole mass, an increasing Maxwellian electrical charge with cosmic time and a time-dependent brahe tension. The cosmological model exhibits several features of cosmological and astrophysical interest for both the early and late universe consistent with recent observations, in particular the ones concerned with the gravitational constants, black holes masses and charges and variation of the gauge coupling parameters with cosmic time. One interesting mark of the constructed model concerns the fact that a black hole mass surrounded by quintessence energy may increase with time even if the horizon disappears.

Eliminating Black Holes Singularity in Brane World Cosmology

In recent works, a construction was proposed resulting in emergent universes inside black holes. This result can be obtained from a 4D black hole embedded in a 5D spacetime with the fifth dimension compactified on a circle [0, 2] (0 and 2 are identified) such that the two branes are at 0 and 1. In the present work, we study this setup by deriving particles’ equations of motion in the new universes, based on redefining energy and angular momentum. This leads to disappearance of the singularity in centers of black holes in classical General Relativity.

Trials to Resolve Black Holes Instabilities in Brane World Cosmology Models

In this letter, we report on our trials to remove the instability of black holes in brane world cosmological models consisting of two branes and a bulk. In order to resolve this problem, general types of interaction potentials were employed. Careful analyses have shown that although the black holes instabilities were removed, a sort of arbitrariness adherent to the motion of the two branes towards each other has taken place leading to an unstable system. Thus, the models seem to us rather paradoxical.

About Worlds inside a Black Hole and Peculiarities of the Formation of Exotic Space Objects

The article puts forward a hypothesis about the possibility of the existence of our Universe inside a supermassive black hole, analyzes the basic assumptions and verifiable physical consequences. The transformation of the Primary Particles obtained from the decay of Borromeo rings into binary and ternary structures is considered separately, taking into account how the percentages between Dark Matter, Dark Energy and Baryonic matter are formed. A system of kinetic equations has been compiled, which makes it possible to develop a theoretical approach to obtain these values depending on the geometric and physical characteristics of interacting particles. The possibility and necessity of the existence of a Primary Relic of Primary Particles are substantiated. The nature of the voids and the analytical solution of the Einstein equations obtained from the generalized Papapetrou solution, which leads to the existence of strings with an arbitrary distribution of matter along the string and with lengths comparable to the size of the Universe, are considered. In the case of a string of finite size and constant density, this solution leads to the well-known Weyl solution. An assumption is put forward about the existence of an Einstein-Rosen type transition, when the dimensions of the white and black holes at the ends of this transition have different dimensions.

彩虹黑弦的热力学性质（英文）

双重相对论(DSR)是描述平直时空中的量子引力的一个有效模型.当试图将该模型纳入到弯曲时空中考虑时,一种被称为"彩虹引力"的理论可帮助实现这一推广,此时背景时空依赖于探测粒子的能量.事实上受粒子能量影响的度规的形式依赖于正交系的选取.本文主要考虑了自由落体参考系下的彩虹静态柱对称黑洞(彩虹黑弦).得到了取一阶近似的彩虹黑弦的霍金温度和熵,这种修正来源于考虑的彩虹引力效应.

无限长带电旋转的稳态黑弦的自发辐射

本文研究了奇异黑弦的自发辐射,得到了辐射粒子的能量范围,指出自发辐射是一切拖曳或带电视界存在的普遍性质。

5维黑弦时空中标量场辐射的数值解

使用无质量的标量粒子作为检验粒子,研究它在5D黑弦背景时空中的运动以及额外第五维对Hawking辐射的影响.经过乌龟坐标变换后,径向方程变成一个类Schrdinger形式的主方程.在求解粒子的径向运动之前,我们针对Nariai黑洞的极端情况来确定参数,然后确定边界条件并采用了多项式近似,最后利用数学软件求得了粒子径向运动的数值解.从最终的结果来看,粒子在视界之间的波形近似谐波,并且在接近视界处波形迅速堆积起来.

On stability behaviors of 5D M-theory black objects

Using N=2 supergravity formalism,we investigate certain behaviors of five-dimensional black objects from the compactification of M-theory on a Calabi-Yau three-fold.The manifold has been constructed as the intersection of two homogeneous polynomials of degrees(ω+2,1)and(2,1)in a product of two weighted projective spaces given by WP^(4)(ω,1,1,1,1)×P^(1).First,we determine the allowed electric charge regions of the BPS and non BPS black holes obtained by wrapping M2-branes on appropriate two cycles in such a proposed Calabi-Yau three-fold.After that,we calculate the entropy of these solutions which takes a maximal value corresponding to ω=1 defining the ordinary projective space P^(4).For generic values of ω,we show that the non BPS states are unstable.Then,we conduct a similar study of five-dimensional black strings.Concerning the allowed magnetic charge regions of the BPS and non BPS black stringy solutions derived from M5-branes on dual divisors,we calculate the tension taking a minimal value for P^(4).By determining the recombination factor,we show that the non-BPS black string states are stable in the allowed regions in the magnetic charge space.

2维弦论中的黑洞的熵

在2维弦论黑洞背景时空中求解了具有’tHooft的边界条件和“准周期”边界条件的Klein－Gordon方程和Dirac方程，分别计算了相应的玻包子熵和费米子熵，发现它们具有同一发散形式，两者仅相差一个系数。

五维黒弦的热力学性质和热力学几何性质

计算了五维黒弦的热容量和电容率;获得了五维黒弦的Ruppeiner几何和Weinhold几何的度规,并指出二者度规不存在共形的关系.

黑弦的热效应与卡诺循环

通过计算表明，奇异的黑弦和普通黑洞一样，具有类似的量子热效应．指出看到热辐射的观察者均不在无穷远处．

Geodesics of Spherical Dilaton Spacetimes

The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesics. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant α are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for α≠ 0.

弦论中的黑洞熵作为熵概念教学的一个实例

带两种荷的束缚态D1-D5膜体系是弦论中最简单的一种黑洞模型。本文将这种体系的熵计算问题介绍给感兴趣的老师和同学,希望为热力学与统计物理中熵的教学提供一个尽可能接近现代物理研究前沿的真实例子。

Thermodynamics of a Schwarzschild Black Hole With a Cosmic String or a Global Monopole

It is well known that thermodynamics of the black hole whose space-time isasymptotically flat obeys the four laws proposed by Bardeen, Carter and Hawking.But for the Schwarzschild type black hole whose space-time is no longerasymptotically flat, whether the Bardeen-Carter-Hawking laws are valid is worthstudying. We all know that certain gauge theories allow possibility of topological de-

黑弦的热效应与卡诺循环的研究

通过计算表明，奇异的黑弦和普通黑洞一样，具有类似的量子热效应，指出看到热辐射的观察者均不在无穷远处。