黑洞熵、膜世界和熵引力若干问题的研究

发布时间：2018-03-22 06:38

本文选题：黑洞熵　切入点：拓扑相变　出处：《上海大学》2011年博士论文　论文类型：学位论文

【摘要】：在现代物理学的发展中,有许多方向可能进一步改变我们的时空观念,这些方向包括黑洞理论、额外维理论和引力熵力学说。论文的三个部份分别探讨了这三个方向的课题。第一部分使用Hopf指数定理分别研究了两种黑洞——4-维轴对称黑洞和NUT-Kerr-Newman黑洞的熵的拓扑起源和相变问题,计算了两种黑洞在不同拓扑状态下的Euler示性数,得到了不同状态下Kerr-Newman黑洞的熵0、A/4和NUT-Kerr-Newman黑洞的熵0、A/16、3A/16、A/4,指出了从恒星演化的这两种黑洞的一级拓扑相变的相变潜热都在γ爆的能量级范围10 51 ergs→1054ergs内,因此从恒星演化的黑洞一级拓扑相变是γ爆的可能成因之一。第二部分在具有微小的倾斜额外维、很小的、静态radion场的五维膜世界中,推导了四维爱因斯坦方程的低能有效形式。接下来展示了首阶上的类Israel联结条件,正是它导致可以从交叉度规得到传统的牛顿常数。在额外维与时间横截且空间平坦的膜上以及低能情况下,得到了标准的费雷德曼方程。发现正是牛顿常数暗示了新增的额外维倾斜的条件。指出若倾斜非常小,对应的宇宙是刚性(stiff)流体主导的;若倾斜增加一点点,则理论上当前宇宙可以有一个自加速过程。最后,得到了五维爱因斯坦方程在全时空的一个简单解,并阐明了这个宇宙在当前加速而在不久之前减速膨胀。第三部分从两种典型的修正引力理论——Gauss-Bonnet引力和f(R)引力——的场方程出发研究了n维球对称时空中引力作为熵力出现的问题。在Gauss-Bonnet引力中,分别在静态和动态时空背景下分离出了熵力项naFa,得到了相应的自引力修正因子χGB,χGB’;在f(R)引力中,则分别在静态时空和FRW宇宙背景下分离出了熵力项naFa,分别得到了相应的自引力修正因子χf(R),χf(R)’。在Gauss-Bonnet引力中,静态和动态情况具有相同的修正因子,而在f(R)引力中并非如此。在Gauss-Bonnet引力中的n维时空下推导了Wald-Kodama熵,并在f(R)引力中分别在n维静态时空和FRW时空下得到了广义Misner-Sharp能量。
[Abstract]:In the development of modern physics, there are many directions which may further change our space-time concept, including the theory of black hole, the theory of extra dimension and the theory of gravitational entropy mechanics. In the first part, the topological origin and phase transition of entropy of two kinds of black holes, 4-dimensional axisymmetric black holes and NUT-Kerr-Newman black holes, are studied by using Hopf exponent theorem, respectively. The Euler representation numbers of two kinds of black holes in different topological states are calculated. The entropy of Kerr-Newman black hole in different states and the entropy of NUT-Kerr-Newman black hole in different states are obtained. It is pointed out that the phase transition latent heat of the first order topological phase transition of these two black holes from stellar evolution is in the energy level of 10 51 ergs. 鈫扞n 1054ergs, the first-order topological phase transition of the black hole evolving from the star is one of the possible causes of 纬 -explosion. In the second part, the low-energy efficient form of the four-dimensional Einstein equation is derived in the five-dimensional film world with small, small, static radion field with small tilted extra dimension. Then, the first-order Israel like coupling conditions are shown. It is because of this that the traditional Newtonian constant can be obtained from the crossover metric. In the case of an extra dimension and time transected and spatially flat film, and in the case of low energy, The standard Free-#internal_person0# equation is obtained. It is found that the Newtonian constant implies the condition of the additional dimension tilting. It is pointed out that if the tilt is very small, the corresponding universe is dominated by rigid fluid; if the inclination increases a little bit, Finally, a simple solution of the five-dimensional Einstein equation in the whole space and time is obtained, and it is clarified that the universe is accelerating at present and decelerating expansion not long ago. In the third part, starting from the field equations of two typical modified gravitational theories, Gauss-Bonnet gravity and fen R gravitation, the problem of the presence of gravity as entropy force in n-dimensional spherically symmetric spacetime is studied. In Gauss-Bonnet gravitation, The entropy force term nafa has been isolated under the background of static and dynamic space-time, respectively, and the corresponding self-gravity correction factor 蠂, 蠂 ~ (GB) is obtained, and in the case of fen _ r _ () gravity, the corresponding self-gravity correction factor (蠂 ~ (GB)) is obtained. Then the entropy force term NaFaa is separated from the static space-time and FRW cosmic background respectively, and the corresponding self-gravity correction factors 蠂 ~ F ~ (1) R ~ (1), 蠂 ~ (f) ~ (1) R ~ (1) are obtained, respectively. In Gauss-Bonnet gravity, the static and dynamic conditions have the same correction factor. The Wald-Kodama entropy is derived in the n-dimensional spacetime of Gauss-Bonnet gravity, and the generalized Misner-Sharp energy is obtained in the n-dimensional static spacetime and FRW spacetime respectively.
【学位授予单位】：上海大学
【学位级别】：博士
【学位授予年份】：2011
【分类号】：P145.8

【共引文献】