On Investigation Of The Relativistic Compact Objects

Black hole,topological defect and soliton star are three kinds of relativistic compact objects,which is a hotpoint of investigation in cosmology and astrophysics. A black hole is not only a solution for the Einstein's equation,but also it is a simple and elegant celestial body,in the sense that only a few parameters,like mass,charge and angular momentum are enough to describe it.One of major motivations to study quasinormal modes of black hole is to estimate black hole parameters.After perturbing a black hole,there is a quasinormal ringing outside the black hole.The frequency and damping of the 'ring' depend only on the structure of the background spacetime.Topological defects originated from phase transitions in the early universe. Of particular interest for cosmology is the theoretical expectation that at high temperature,symmetries that are spontaneous symmetry breaking(SSB) today were restored,and that during the evolution of universe there were phase transitions.On the other hand,there are the topological defect solutions in the SSB relativistic field theories.Topological defects are invoked to explain a variety of cosmic enigmas, including the large-scale structure of cosmic,the baryon asymmetry,etc.In relativistic non-linear field theory,topological defects are a kind of topological soliton.Soliton star is a soliton with star mass and star size.It maybe formed in the early universe and is a candidate for dark matter.Here,the relations between quasinormal modes of small AdS-Schwarzschild black hole,stringy black hole and acoustic black hole and their parameters are discussed,respectively,and the effect of quintessence on the global monopole is also considered.In this paper,there are four sections.In section one,we have a brief review of black hole,topological defect,soliton star.In section two,we introduce two numerical methods to calculate quasinormal modes of a small Schwarzschild black hole.One is the ordinary finite element method.The other is Frobenius method.We find that the oscillating quasi-period and the imaginary part of the fundamental quasinormal modes (n=0) decrease with a decrease of the event horizon;the oscillating quasi-period and the damping time scale decrease as the multipole index increases.Furthermore,the real part and the imaginary part of the quasinormal frequency increase with an increase of n.Then,using the ordinary finite element method,the relation between quasinormal modes of stringy black hole and its parameters is discussed.In 1+1 dimensional stringy black hole spacetimes,the oscillating quasi-period decreases as the mass increases,but the damping time scale slightly increases with the mass.The oscillating frequency and the damping time scale are both increasing as the parameter Q increases.In 1+3 dimensional stringy black hole spacetimes,the oscillating time and the damping time increase with an increase of the event horizon.In section three, we study the quasinormal modes and late-time tails of a canonical acoustic black hole. Acoustic black hole is an analogue black hole made in the laboratory.We show the relations between quasinormal modes of the canonical acoustic black hole and its parameters.And we also study its late-time tails.For l≥2,the numerical results are consistent with the first,third and sixth orders WKB method,and show that the late-time tail decays as the power-law falloff of the formΦ≈7.36×10^-32t^-10.The oscillating quasi-period and damping time scale are both increase with the angular momentum l.In the limit of large l,the real part of fundamental quasinormal frequency increases linearly and imaginary part tends to a constant with the angular momentum.In section four,we investigate new static spherically-symmetric solutions of Einstein equations with a global monopole surrounded by quintessence.The new solutions are more complicated,which depend on the parameter of equation of state Wq.We show that the gravitating global monopole produces a gravitational field of de Sitter kind outside the core in addition to a solid angular deficit.Furthermore,W_q= -1/3 solution cannot exist because the density of quintessence tends to zero as W_q→-1/3.The new feature is the appearance of outer horizon for the case of a global monopole surrounded by quintessence.