三阶Lovelock引力中的黑洞

发布时间：2018-08-18 12:30

【摘要】：在平坦(flat)和反德西特(Anti-de Sitter)时空中,本文分别求出了三阶Lovelock静态黑洞解并计算了黑洞的质量,温度和熵。取Gauss-Bonnet和三阶Lovelock项的特殊系数,继而得到了在两种时空中特殊的黑洞解。根据这两个特殊解,分别在Gauss-Bonnet项的系数为正值(α20)和负值(a20)的两种情况下对黑洞进行了热力学分析。对于平坦时空的三阶Lovelock黑洞,我们基于哈密顿-雅克比方法求出了在七维时空的黑洞的温度和熵的修正。对于正的常曲率超曲面,即k=1,当α20在七,八和九维时空中的黑洞存在一个中间稳定相。而在更高维时空,不存在黑洞解。当a20,在系数取不同值时黑洞存在内外两个视界,极端黑洞或者裸奇点。而对于负的常曲率超曲面,即k=-1,在α20和a20的两种情况下都不存在黑洞解。对于反德西特时空的三阶Lovelock黑洞,存在三种不同的视界结构k=0,±1。当k=-1,取a20的黑洞在整个区域都是热力学稳定的,而黑洞(a20)存在一个中间不稳定相。对于正的常曲率超曲面,即k=1,七维时空的黑洞(a20)存在一个中间不稳定相；在八维时空,当|α2|小于某一个值时,黑洞存在两个热力学不稳定区域。这与更高维时空的热力学稳定性区域是相类似的。对于a2O,在系数较小时,球形的七维黑洞存在一个中间不稳定相,而在系数较大时,黑洞则全局稳定。而在更高维时空,黑洞都存在一个中间不稳定相。另外,黑洞的热力学性质和守恒量在k=0时都不依赖于Lovelock系数并且退化到了广义相对论的情形。由于Lovelock引力运动方程的高度非线性,很难获得黑洞转动解的简洁表达形式。通过在一个静态的系统中引入一个小的角动量,我们可以来研究缓慢转动的Lovelock黑洞,并且发现运动方程的tφ分量涉及函数g(r)和c(r)。此外,电磁场张量的非对角分量与函数c(r)有关。在考虑作用量具体表达式,最终得到带电的Gauss-Bonnet缓慢转动黑洞的解析解；并且应用这一方法得到不带电和带电的三阶Lovelock黑洞的缓慢转动解。随后分别计算了Gauss-Bonnet和三阶Lovelock黑洞的角动量,磁偶极矩和磁旋回比率,发现这些高阶导数曲率项并不影响黑洞的磁旋回比率。另外,如考虑Lovelock作用量的更多相关项,想要通过运动方程求解缓慢转动解是非常困难的。但是通过作用量直接变分,得到了在平坦时空中的Gauss-Bonnet黑洞的缓慢转动解。我们发现当黑洞的转动不是非常缓慢的时候,黑洞的视界和无限红移面不再重合。
[Abstract]:In the flat (flat) and Anti-de Sitter spacetime, the third-order Lovelock static black hole solution is obtained and the mass, temperature and entropy of the black hole are calculated. By taking the special coefficients of Gauss-Bonnet and third-order Lovelock terms, we obtain the special solutions of black holes in two kinds of space-time. According to these two special solutions, the thermodynamic analysis of the black hole is carried out under the condition that the coefficients of the Gauss-Bonnet term are positive (伪 20) and negative (a 20), respectively. For the third-order Lovelock black hole with flat spacetime, the temperature and entropy of the black hole in 7-dimensional spacetime are modified based on the Hamilton-Jacobian method. For a positive hypersurface of constant curvature, that is, KG 1, there is an intermediate stable phase for a black hole with 伪 20 in seven, eight, and nine dimensional spacetime. In higher dimensional spacetime, there is no black hole solution. When a 20, the black hole exists inside and outside two event limits, extreme black hole or bare singularity when the coefficient is different. However, for negative hypersurfaces of constant curvature, that is, KG -1, there is no black hole solution in the case of 伪 20 and a 20. For the third-order Lovelock black hole in anti-de Sitte spacetime, there are three different event horizon structures K0, 卤1. The black hole (a20) is thermodynamically stable in the whole region, and the black hole (a20) has an intermediate unstable phase. For the positive hypersurface of constant curvature, that is, the black hole (a20) of KG 1, 7 dimensional spacetime, there is an intermediate unstable phase, and in 8 dimensional spacetime, when 伪 2 is less than a certain value, the black hole has two thermodynamically unstable regions. This is similar to the region of thermodynamic stability of higher dimensional spacetime. For a _ 2O, there is an intermediate unstable phase in the spherical seven-dimensional black hole when the coefficient is small, but when the coefficient is large, the black hole is globally stable. In higher dimensional spacetime, black holes have an intermediate unstable phase. In addition, the thermodynamic properties and conserved quantities of black holes are independent of Lovelock coefficients and degenerate to the case of general relativity when k = 0. Because of the high nonlinearity of the Lovelock equation of gravitational motion, it is difficult to obtain the simple expression of the black hole rotational solution. By introducing a small angular momentum into a static system, we can study the slowly rotating Lovelock black hole and find that the t 蠁 component of the equation of motion involves functions g (r) and c (r). In addition, the non-diagonal component of the electromagnetic field Zhang Liang is related to the function c (r). The analytical solution of the charged Gauss-Bonnet slowly rotating black hole is obtained by considering the concrete expression of the action quantity, and the slow rotation solution of the uncharged and charged third-order Lovelock black hole is obtained by using this method. Then the angular momentum, magnetic dipole moment and magnetic cycle ratio of Gauss-Bonnet black hole and third-order Lovelock black hole are calculated respectively. It is found that these higher-order derivative curvature terms do not affect the magnetic cycle ratio of black hole. In addition, it is very difficult to solve the slow rotation solution by the equation of motion if we consider more related terms of the Lovelock action. However, the slow rotation of Gauss-Bonnet black hole in flat spacetime is obtained by direct variation. We find that the event horizon of the black hole and the infinite redshift surface no longer coincide when the rotation of the black hole is not very slow.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：P145.8

【共引文献】