The Fastest Relaxation Of Born-infeld Black Hole

Isolated black holes in equilibrium can be described by only a few parameters such as their mass,angular momentum,and charge.So,they are much simpler than ordinary matter around us.Howener,a real black hole can never be fully described by its basic parameters and is always in the perturbed state.Once a black hole is perturbed it responds to perturbations by emitting gravitational waves whose evolution in time can be conditionally divided into three stages:(1)a relatively short period of initial outburst of radiation,(2)usually a long period of damping proper oscillations,dominated by the so-called quasinormal modes,and(3)at a large time the quasinormal modes are suppressed by power-law or exponential late-time tails.Black hole quasinormal modes describes the characteristic perturbation oscillations of black holes,which can be obtained by solving the corresponding equations of the fields endowing with appropriate boundary conditions.In general,we impose the purely outgoing waves at spatial infinity and purely ingoing waves at the black hole event horizon.Then solving the perturbation equations,one can obtain a set of discrete complex quasinormal mode frequency ?nwith n the discrete overtone number.Its real part denotes the oscillations of the perturbations,while the imaginary part corresponds to the decay of the amplitude.On the other hand,the imaginary part of fundamental quasinormal mode(n = 0)frequency has a relation to the characteristic relaxation time of the black hole system.In 1934,Born and Infeld proposed a nonlinear electrodynamics with the aim of obtaining a finite value for the self-energy of a point-like charge.In the limit b = 0,Born-Infeld theory reduces to the standard Maxwell thory.The Born-Infeld black hole is the most known solution of Einstein–Born–Infeld theory.In this thesis,we study the relaxation rate for the Born-Infeld black holes with nonlinear electromagnetic field.The quasinormal resonance frequencies for massless scalar perturbations are analytically calculated in the eikonal regime.For the Born-Infeld parameter b < bc with bc a critical value,the fastest relaxation rate always occurs near the black hole charge Q = 0.72 ? 0.78.While for b > bc,the fastest relaxation rate is found near the extremal Schwarzschild black hole with vanishing horizon.Comparing with the charged Reissner-Nordstr ¨om black hole,we find that the black hole with non-vanishing charge has the fastest relaxation rate in small b range.Moreover we find that the Born-Infeld parameter increases with the black hole charge relating with the fastest relaxation rate and the relaxation rate and the fastest relaxtion rate slightly with increasing parameters.These results uncover the significant property of the relaxation rate in Born-Infeld theory.I also explore the relaxtion rate of the Born-Infeld de Sitter black hole with different cosmological constant.