Research On The Correlation Between Curved Spacetime And Quasi-normal Scale Of Black Hole

Black hole is a significant prediction of the general relativity.As the solution of Einstein’s field equation,it plays a vital role in modern physics.The shooting of the pic-ture of Sagittarius A*confirmed the existence of the black hole.The gravitational waves produced by the merger of black holes have also been directly observed by LIGO/Vir-go,and with the improvement of observation accuracy,more and more gravitational wave events have been detected,which also brings us into the era of multi-messenger astronomy.These recent observations have opened up entirely new avenues for studying gravitational interactions.The gravitational waves emitted by black holes,neutron stars or other compact objects carry the unique characteristics of themselves and their envi-ronment,so gravitational wave signals are expected to be used to detect and distinguish different compact objects,and the research on gravitational waves will also help us to further deepen our understanding of the gravity theory.The commonly used method to study the physical properties of black holes is black hole perturbation.The black hole will respond to the perturbation by emitting gravitational waves.The time evolution of gravitational waves will go through three stages:first is a relatively short initial radiation burst stage;then longer damped oscillations,i.e.the so-called quasinormal modes（QN-Ms）;finally the exponential decay of the quasinormal modes.The quasinormal mode is the characteristic oscillation mode of a black hole.Since the quasinormal modes can only be determined by the parameters of the black hole itself,it is crucial for us to un-derstand the dynamics of black holes,and it is also an important link between gravity and quantum mechanics.In this thesis,we study the quasinormal modes of several spherically symmetric black hole solutions.Especially,in the Black-bounce spacetime,we find the gravitational wave echoes signal behind the initial ringdown.This unique gravitational wave feature is important for studying whether the event horizon of a black hole has quantum properties.In future astronomical observations,the corresponding black hole can be detected by identifying the gravitational wave echoes signal.The specific study content of this thesis is as follows:Firstly,we study the oscillators in two types of curved spacetime（G¨odel-type space-time and Som-Raychaudhuri spacetime）.The main content is to subtly simplify the field equation into a solvable wave equation under the curved spacetime background,and then the corresponding wave equation is solved by mathematical methods to obtain the energy spectrum and wave function of the oscillator in the curved spacetime background,which enables us to better understand the nature of curved spacetime.Meanwhile,it has laid a solid mathematical foundation for us to study the quasinormal modes of black hole spacetime.Secondly,we study the quasinormal modes of a hairy black hole under the external field and the axial gravitational perturbations.According to the spacetime line elements of hairy black holes,we obtain the effective potential functions under scalar field pertur-bation,electromagnetic field perturbation and axial gravitational perturbation.Using the finite-difference method,the influence of the hairs（,7）₀,)of a hairy black hole on the time evolution of the gravitational wave signal under three perturbations is studied.To obtain the QNM frequencies,we extracted the QNM frequencies from the ringdown using the Prony method,and also verified the accuracy of the frequency using the WKB method.By analyzing the influence of hairs,7)₀andon the QNM,we find that hairsand7)₀reduce the oscillation frequency of the gravitational wave signal,whileincreases the oscillation frequency.In addition,we use the Sinc approximation to study the greybody factor and the high-energy absorption cross-section of a hairy black hole.Our results show that the existence of hairsand7)₀can increase the probability of gravitational radiation reaching spatial infinity,while the contribution of the hairis the opposite.Finally,we study the evolution of gravitational waves in the black-bounce spacetime under the electromagnetic field perturbation and scalar field perturbation.We find that when 0<(6<2the spacetime is a regular black hole,when(6=2the spacetime is a one-way wormhole,and when(6>2the spacetime is a two-way traversable wormhole.The ringdown of the black-bounce spacetime in these three cases is given by the finite difference method,and we find that the spacetime has gravitational wave echoes signals only when(6>2.But when the parameter(6 continues to increase,the echoes signal will become weaker and weaker,and finally become the quasinormal ringdown of the two-way wormhole,and no longer have the echoes signal.These results show that the gravitational wave echoes signal can be used to distinguish whether the Black-bounce spacetime is a black hole or a wormhole.We also study the effect of string clouds on the near-horizon region by analyzing the QNM of a black-bounce spacetime surrounded by string clouds under scalar field and electromagnetic field perturbations.Our results show that the presence of string clouds will not affect the appearance of gravitational wave echoes in black-bounce spacetime.But the existence of the string cloud makes the threshold value(6₍（8）bigger,that is to say,it changes the parameter space of the black-bounce spacetime.