Research On The Evolution Of Black Holes And The Related Problems Of Gravitational Waves

Black holes are the product of Einstein's general relativity.In the past 40 years,people have made great progress in the study of the properties of black holes.These work and research involve all aspects of physics,which can reveal the nature of physics.However,there are still many problems in the study of black holes.Moreover,some studies of black holes are not complete.Therefore,this dissertation will focus on two aspects.The first aspect is concerned with the evolution of black holes,which including the Hawking radiation and the quasinormal modes of black holes.In the second aspect,the problems that associated with gravitational waves will be discussed.The main content and the result of each chapter contain many new results.The main results are as follows:1.Using a new general tortoise coordinate transformation,the tunneling rate of scalar particles and fermions from the non-stationary higher dimensional Vaidya-de Sitter black hole are studied.Then the Hawking temperature of the non-stationary higher dimensional Vaidya-de Sitter black hole is obtained.Subsequently,we develop Kruglov's theory and investigate the Hawking radiation of vector particles from 4-dimensional Kerr-de Sitter black hole and 5-dimensional Schwarzschild-Tangherlini black hole for the first time via quantum tunneling method.The results show that the tunneling rates and Hawking temperatures are depended on the properties of spacetimes.It shows that the radiation spectrum belongs to the pure thermal spectrum,which would lead to the black hole information loss paradox and naked singularity problem.Meanwhile,we derive the Hamilton-Jacobi equation from the Klein-Gordon equation,the Proca equation,and the Dirac equation.This result is consistent with the previous predictions,which shows that the Hamilton-Jacobi equation is a fundamental equation for studying the Hawking radiation of black holes.2.The thermodynamics of Schwarzschild-Tangherlini(ST)black hole in the context of the generalized uncertainty principle(GUP)is investigated.Using the generalized uncertainty principle,a modified Hamilton-Jacobi equation,which can describe the dynamic behavior of particles with spin 1 and 1/2 in the curved spacetime is derived.Then,the quantum tunneling behavior of particle from horizon of ST black hole is studied.Finally,the corrections to the Hawking temperature,entropy and the heat capacity are obtained.The results show that,if one considers the effect of quantum gravity,the behavior of the tunneling particles on the event is different from the original case.The GUP corrected Hawking temperature is smaller than the original temperature,and the GUP corrected thermodynamic quantities are not only sensitively depended on the mass and the spacetime dimension D of ST black hole,but also on the properties of particles and the quantum gravity term ?.The GUP corrected temperature reaches the maximum value and then decreases to zero when its mass approaches the minimum value of the mass,which is of the order of the Planck scale.Therefore,it predicts the existence of the black hole remnant.For confirming the black hole remnant,the GUP corrected heat capacity has also been analyzed.The result shows that,the behavior of the GUP corrected specific heat is similar to the original case when the mass of the black hole is large enough.By decreasing the mass of the ST black hole,the GUP corrected specific heat becomes smaller and departs from the original ST black hole behavior.The GUP corrected specific heat has a vertical asymptote at Mcr,which means the specific heat changes from negative to positive.Finally,the GUP corrected specific heat decreases to zero as the mass decreases to Mmin.At that point,the black hole cannot exchange its energy with environment,and leads to the black hole remnant.The existence of black holes' remnant implies the black hole wound not evaporate completely.Thus,the Hawking radiation cannot lead to the black hole information loss paradox and naked singularity problem.In addition,this work also shows that the minimum energy to form a black hole is larger than the current energy scales of the LHC.In order to detect the black hole signal,it is necessary to upgrade the LHC.3.We study the perturbation evolution process of a strong gravitational background spacetime,which contains the charge,cosmological constant,and quintessence energy.Using the WKB approximation method,the quasinormal modes(QNMs)is studied in Reissner-Nordstr?m-de Sitter quintessence(RN-dSQ)spacetime.The results show that the RN-dSQ black hole remains stable under the massless scalar field perturbation,the effective potential and QNMs frequency are related to the background spacetime of RN-dSQ black hole.Moreover,by comparing with the results from Reissner-Nordstr?m black hole case,it is easy to find that the quintessence energy and cosmological constant can reduce the effective potential and QNMs frequencies of RN-dSQ black hole.4.The data of gravitational wave event GW150914 is analyzed.It shows that the observed speed of gravitons is less than its theoretical value.In order to solve this problem,we use the generalized uncertainty principle.It finds that the generalized uncertainty principle can significantly reduce the speed of the gravitons.Furthermore,we constrain two kinds of GUP parameters based on t he data of gravitational wave event GW150914,the results implies that the gravitational wave measurements are more suitable for studying effects of the Ali-Das-Vagenas proposal.5.We analyze the formation mechanism of the hypervelocity stars.Meanwhile,the observation of hypervelocity stars is also summarized.The results show that most of the hypervelocity stars are ejected by the supermassive black hole in the galactic center.By using the observation data of these hypervelocity stars,one can analyze the structure of the Milky Way.However,it is also find that some hypervelocity stars' formation mechanism is not clear.Therefore,our next research direction will solve those problems.