Some Problems About Entropy Of Black Hole, Braneworld And Entropic Gravity

There are many issues among modern physics which could change our concepts of space-time, including theories of black holes, extra dimensions and entropic force hypothesis. This dissertation discusses these issues respectively in three sections.In the first section, the entropy and phase transition of two types of black holes, 4-Dimensional axisymmetric black hole and NUT-Kerr-Newman black hole, are investigated. The Euler characteristics of these tow black holes in different status are calculated, which lead to the entropy 0, A/4 of Kerr-Newman black hole and 0, A/16, 3A/16, A/4 of NUT-Kerr-Newman black hole in different status. It is pointed out that the latent heat of the typical black hole evolved from the star just lie in the span of the energy of gamma ray bursts 105 1 ergs→1054ergs, which implies the topological phase transition of typical black hole evolved from the star is a optional origin of the gamma ray burst.In the second section, the effective four-dimensional Einstein equation at low energy in five-dimensional brane world with a tinily sloping extra dimension, the trivial , and the static radion field is derived. It is showed that there still is the similar Israel junction condition at leading order, which results a conventional Newton's constant originated from the cross metrics. Then the standard Friedmann equation at low energy for a spatial flat brane with an extra dimension transversal to the time is derived. It is shown that the Newton's constant suggests the increased slope of extra dimension. When the slope is very small, the corresponding universe is found stiff fluid dominated. When the slope increases a little, the theory may provide a self-acceleration of the universe at present epoch. A simple solution of five-dimensional Einstein equation in whole space-time and illustrate a universe which may accelerate at present epoch and decelerate in the very recent past is also obtained.In the third section, the issue that gravity appears as an entropic force from the field equation for two modified gravity theories, Gauss-Bonnet gravity and f(R) gravity, in n-dimensional spherically symmetric spacetime are investigated. In these two typical modified gravity theories, the entropy force term naFa is separated, and the self-gravity modified factorsχGB,χGB',χf(R) andχf(R)'are gotten respectively. For Gauss-Bonnet gravity, the static and dynamic cases have the same modified factors, but not for f(R) gravity. Moreover, the Wald-Kodama entropy for Gauss-Bonnet gravity in n-dimensional spacetime and the generalized Misner-Sharp energies for f(R) gravity respectively in n-dimensional static spacetime and FRW spacetime are derived, which will be useful in the high-dimensional gravitational thermodynamics.