Study On The Stability Of Black Holes Under Bumblebee Gravity Theor

Searching for a unified theory is the ultimate goal of physical research,but general relativity and quantum mechanics are incompatible,which forces people to find new theories of gravity,including quantum gravity.Through the study of quantum gravity,people found that Lorentz symmetry breaking may occur under the Planck scale,and then constructed a series of gravitational theories with Lorentz breaking mechanism,the simplest of which is the Bumblebee gravity.In this theory,a vector field ruled by a potential acquires a nonzero vacuum expectation value,which chooses a preferred spacetime direction in the local frames and spontaneously breaks the Lorentz symmetry.Recently,a series of black hole solutions in Bumblebee gravity theory have been found.The study of black holes has always been the frontier and hot spot in theoretical physics,and the stability of black holes is particularly important.It involves not only the possibility of the actual existence of black holes,but also many other applications,such as studying the new physical effects in modified gravitational theory.In this thesis,we study the dynamic stability of several kinds of black holes in the Bumblebee gravity,including superradiant instability and quasinormal modes.The superradiance of a black hole means that the bosonic field satisfying the super-radiant condition can extract energy（electric charge and angular momentum）from the black hole,resulting in the stronger outgoing wave than the ingoing wave.If the bosonic field is bound near the black hole by some mechanism,the superradiant process will occur repeatedly,resulting in the superradiant instability of the background spacetime.In the second chapter of this thesis,we investigate the superradiant instability of the Kerr-like black holes in Bumblebee gravity under the perturbation of a massive scalar field.Through analytical analysis,We find the Lorentz breaking parameter L does not affect the superradiance regime or the bound state regime,but still affects the bound state spec-trum and the superradiant magnification.We calculate the bound state spectrum via the continued-fraction method and show the influence of L on the maximum binding energy and the damping rate.The superradiant instability could occur since the superradiance condition and the bound state condition could be both satisfied.We find the growth rate of the unstable mode depends nonmonotonously not only on the rotation parameter of the black hole?a and the product of the black hole mass M and the field massμ,but also on the Lorentz breaking parameter L.Through the Monte Carlo method,we find the most unstable mode with the maximum growth rateω_IM=1.676×10^-6,which is about 10times than that in the Kerr black hole.The quasinormal modes of a black hole refer to the medium term oscillation atten-uation behavior of the field around the black hole during its evolution.The quasinormal modes are called as"characteristic sound"of the black hole,because it is only related to the parameters of the black hole itself and independent of the initial disturbance of the external field,and it is expected to be observed in the gravitational wave experiment.Through the study of quasinormal modes of black holes,we can further understand the characteris-tics of black holes and have a deeper understanding of gravitational theory.In the third and fourth chapters of this thesis,we study the quasinormal modes of Schwarzschild-like black holes with global monopole and Schwarzschild-anti-de Sitter black holes with global monopole in Bumblebee gravity theory under the perturbation of a massless scalar field.Using different numerical methods,we investigate the stability of black holes in frequency domain and time domain respectively.We find that these two kinds of black holes are stable under the perturbation of massless scalar field.In addition,the Lorentz breaking parameter L has the same effect on the stability of these two kinds of black holes.The smaller L is,the more stable the black hole is.However,the influence of the global monopole parameterκη²on the stability of these two kinds of black holes is different.For Schwarzschild-like black holes,the largerκη²is,the worse the stability of the black hole is;For the Schwarzschild-anti-de Sitter black hole,the global monopole has little effect on its stability.That is to say,when cosmological constantΛ<0,Lorentz breaking has a significant impact on the stability of the black hole,while the global monopole has a small impact on the stability of the black hole.We have further analyzed this difference.