A Dedicated Study On The Balck Hole Thermodynamics And Dynamics

As the most important prediction of general relativity,black hole has always been the frontier and hot topics in theoretic physics.The study of black hole not only explains many phenomena in astrophysics,but also relates to the semi-classical and quantum gravity theory.An important subject in quantum gravity is the microscopic explanation of Bekenstein-Hawking entropy.Though string theory and loop quantum gravity both proposed convinced but limited explanation,the problem still leaves unsolved.As the rising of holographic principle,the entropy of black hole can be calculated by the quantum field which is dual to the gravity.Kerr/CFT correspondence is one of the method which can be used to calculate the entropy of extremal rotating black hole.The background spacetime they considered is stationary.However,the real black hole is always unstationary due to the radiation or accretion.We generalized Kerr/CFT correspondence to electrovac extremal isolated horizon and derived the microscopic entropy of unstationary black hole.The other way to microscopic entropy of black hole uses the GibbonsHawking surface term of gravitational action.This is based on that the surface term encodes the same amount information of the bulk action.We noticed that only the near horizon geometry is crucial in this method.Then we generalized this method to the case of isolated horizon.So this method also applies to unstationary black hole.We found that in both methods we just mentioned,the black hole entropy is decided totally by its intrinsic geometry.These discoveries will promote our understanding of black hole entropy and inspire the research of quantum gravity.The second part of this thesis devotes to the analysis to black hole stability.The perturbation not only relates to the possibility that whether or not the black hole exist in real world,but also contributes to many other subjects,such as to distinguish the various modified gravity models.The modified gravity models are inspired by astronomy observation and theoretic research.One of these is the scalar-tensor theory.The scalar-tensor theory and general relativity have the same Kerr-de Sitter(dS)black hole solution.However,we found that there are instabilities caused by superradiance and spontaneous scalarization in scalar-tensor theories.These instabilities do not occur in general relativity.So we can distinguish scalar-tensor theory from general relativity.We discussed the the influence of positive cosmological constant and the angular momentum of black hole on the instability of black hole.We also found a special spontaneous scalarization in dS spacetime which is different from that in flat spacetime.There are results state that almost all the black hole are stable under the neutral scalar perturbation.However,the charged black holes in anti-dS(AdS)spacetime are unstable under charged scalar perturbation.This instability is caused whether by the special structure of AdS spacetime or it can be found in other 4-dimensional spacetime? We studied the stability of4-dimensional stringy dilaton black hole discovered by Garfinkle,Horowitz and Strominger(which is also called as GHS black hole)under charged scalar perturbation.It turns out that the GHS black hole is stable under charged scalar perturbation.This result is different from those in dS or AdS spacetime.We claimed further that superradiant instability can not occur in GHS black hole background.Our result shows the influence of cosmological constant on the stability of black hole.The black hole perturbation is studied by linear analysis.The third part of the thesis studied the gravitational collapse of charged scalar by nonlinear calculations.It turns out that the positive cosmological constant hinders the collapse of matter.While the repulsion of charge can even prevent the formation of black hole.We found that the qualitative property of gravitational collapse is independent of the dimension of spacetime.While the stability of the spherical charged black hole in dS spacetime depends on the dimension of spacetime.These results disclose the important influence of positive cosmological constant and charge.