Black Hole Quasinormal Modes And Black Hole Entropy

The quasinormal modes of black holes and the black hole entropy have longbeen the important parts of the black hole physics. It is well known that thequasinormal modes are closely related to the observation of black holes, and canbe detected through gravitational wave detectors in the near future. Moreover,the results obtained recently show that the quasinormal modes are also related tothe quantum gravity. Therefore, a great deal of efforts have been devoted to theblack hole quasinormal modes. While black hole entropy have long been a puzzledproblem to most theoretical physicists. It is helpful for the development of theblack hole physics and the to study the origin of the black hole entropy. Thisthesis is devoted to investigating the relation between the quasinormal modesand the quantum gravity by studying the behavior of the quasinormal modes atlowing modes and highly damped overtone, and trying to find a possible way ofsolving the origin of the black hole entropy.The thesis consists of five parts. The first part is the introduction; the secondpart is about the low lying quasinormal modes of black hole; the third part isabout the highly damped quasinormal modes of black hole; the fourth part isabout the relation between black hole entropy and the generalized uncertaintyprinciple. Summary of thesis and expectation of future research are given in thelast section.In Sec. I, a brief introduction of black hole's definition, importance andmethods used in studying the quasinormal modes are given.In Sec. 2, we first adopt potential approximation methods (including thethird order WKB approach and the Poschl-Teller aprroach) to study the massivescalar fields and Dirac fields quasinormal modes of the charged black hole instring theory (Garfinkle-Horowitz-Strominger black hole). Then we discuss thequasinormal modes of Schwarzschild black hole due to arbitrary spin fields. Theresults show that the boson perturbations and the fermion perturbations behavein a totally different way. The last section of this chapter is about the quasinormal modes due to the high spin field. The results show that the real parts of thefrequencies increase with the charge,while the dampings almost keep unchangedas the charge increases.In Sec. 3, we study analytically quasinormal modes in a wide variety ofblack hole spacetimes, including d-dimensional asymptotically fiat spacetimesand non-asymptotically fiat spacetimes (particular attention has been paid to thefour dimensional case). We extend the analytical calculation to include first-ordercorrections to analytical expressions for quasinormal mode frequencies by makinguse of a monodromy technique. All possible type perturbations are included inthis paper. The calculation performed in this paper show that systematic ex-pansions for uncharged black holes include different corrections withthe ones forcharged black holes. This difference makes them ha.re a different n-dependencerelation in the first-order correction formulae. The method applied above in cal-culating the first-order corrections of quasinormal mode frequencies seems to beunavailable for black holes with small charge. This result supports the Neitzke'sprediction. On what concerns quanturn gravity we confirm the view that the In 3in d=4 Schwarzschild seems to be nothing but some numerical coincidences.In Sec.4, the entropy of rotating Kerr-Newman-Kasuya black hole dueto massive charged fields (bosons and fermions) is calculated by using the newequation of state density motivated by the generalized uncertainty relation. Theresult shows the entropy does not depend on the mass and the charge but theparameterλ, the area A and the spin of the fields.