The Study Of Black Hole Based On Space-Time-Matter Theory And Brane World

Since in 1920s Kaluza and Klein had unified successfully gravity field and electromagnetic field,the higher dimensional gravitational-field theory came within people's range of vision. Recently,with the small-scale Big Bang model—Large Hadron Collider(LHC) being in operation,the extra dimensional small black hole is very likely to be produced by the collision of particles.Meanwhile,there are two famous theoretical models—Arkani-Hamed, Dimopoylos,Dvali(ADD) and Randall-Sundrum(RS) are developed in the turn of the century.So the developments of theory and experiment set off a new wave of researching extra dimension.In this thesis,the study object is a kind of extra dimensional black hole in which standard model fields(such as fermions,gauge bosons fields) are confined on a(3+1) dimensional hypersurface(3-brane) without accessing along the transverse dimensions.The branes are embedded in the higher dimensional space(bulk),in which only gravitons and scalar particles without charges could propagate under standard model gauge group.If matter trapped on the brane undergoes gravitational collapse,a black hole will form naturally and its horizons extends into the extra dimension which is transverse to brane.Such higher dimensional object looks like a black hole on the brane is actually a black string in the higher dimensional brane world.Hence a 5D Ricci-flat black string is obtained naturally.On the brane the space gives a SdS geometric construction.Specifically,this thesis is organized as follows:the former three chapters are the background knowledge concluding black hole and cosmological constant(chapter 1),higher dimensional gravitational-field theory(chapter 2),brane world(chapter 3);the last four chapters are our work concluding black hole radiation(chapter 4),black hole entropy(chapter 5),real scalar field evolution(chapter 6) and quasi-normal modes(chapter 7).In the respect of black hole radiation,as the equations are coupled,it is found that the structure of the fifth dimension(as for membrane and induced-matter theory) affects the nature of the radiation observed in four-dimensional space-time.From these study it is known that the potential function of radiation equation contains a key parameter from extra dimension.This parameter divides the whole radiation into two parts,one is continuous spectrum and the other is discrete one. The respect of black hole entropy is studied from two sides:one is Thin-Layer Approach (TLA) and the other is Generalized Uncertainty Principle(GUP).In the TLA case,the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method.The modes along the fifth dimension are semi-classically quantized by Randall-Sundrum mass relationship.The two-dimensional area is used to describe this black string's entropy which,in the small-mass approximation,is a linear sum of the area of inner and outer horizons.The proportionality coefficients of entropy are discretized with quantized extra dimensional modes.The smallmass approximation is naturally justified by the assumption of far apart two branes.In the GUP case,entropy is obtained without any cutoff and any constraint on the bulk's configuration rather than the usual uncertainty principle.The system's density of state and free energy are convergent in the neighborhood of horizon.The small-mass approximation is determined by the asymptotic behavior of metric function near horizons.In the respect of real scalar field evolvement,the tangent approximation is chosen to unite tortoise coordinate and radial coordinate,which have transcendental function relationship, in Schr(o|¨)dinger-type equation.The numerical solutions of two extreme cases(∧₁=10^-3 and∧₂=0.11) are obtained.In the case of∧₁,the inner and outer horizons are widely separated. Due to the penetrating power is weak,waves are concentrated near cosmological horizon and become much sparser near even horizon than that of 4D case.In the case of∧₂,two horizons are close to each other.Waves are concentrated near black hole even horizon and the stacking density is larger than that of outer cosmological horizon.In the respect of quasi-normal modes,by using the classical third-order WKB approximation, the evolution of frequencies is carefully analyzed in two aspects,one is the induced cosmological constant and the other is the quantum number n.The massless scalar field decays more slowly because of the existence of the fifth dimension and the induced cosmological constant.Especially,the effect of resonance slows down the decaying of high-frequency.