Studies On The Properties Of Spherically Symmetric Black Hole In The Framework Of GBD Modified Gravitational Theory

Einstein proposed the theory of general relativity（GR）in 1915,which is considered to be one of the most graceful theories in physics.Although GR has achieved great success,studies on gravitational theory has not stopped here.Many problems existed in gravitational physics and the exploration of the essence of gravitational interaction have led to the study of the modified theory of general relativity,which has been a hot issue that people have been working to explore.In this thesis,we mainly study the relevant properties of spherically symmetric black holes in the generalized Brans-Dicke（GBD）modified gravitational theory.The first section in this thesis is the introduction.In this part,we will briefly describe the relevant contents of the development of general relativity and black hole physics.The second part of the thesis mainly introduces the relevant contents of the research on the stability of black-hole physics,including the application of the Lyapunov exponents method and geodesic deviations method to determine the geodesic-motion stability of particles in different black holes and theories.In the third section,we briefly introduce the logarithmic correction of the black hole entropy,and take the d-dimensional RN black hole and the three-dimensional non-rotating BTZ black hole as examples to show the specific expressions for correction entropy of black hole.The fourth part is the major work during the period of my postgraduate.Obviously,it is important to study the structure of geodesic in the strong gravitational field for exploring the physical characteristics of compact object.Firstly,we study the stability of geodesic motion of particles in static spherically symmetric black holes under the framework of GBD modified gravity.Concretely,we analyze the dependence of the innermost stable circular orbit on the model parameters in this thesis.In addition,the geodesic deviation equation method is also applied to discuss the stable circular orbit of the test particle in GBD theory.We exhibit the conditions for the stability of the black hole solution and constrain the radial coordinates by requiring particle to achieve the stable circular orbit motion in GBD theory.Secondly,considering that black hole entropy and entropy correction have always been one of the important topics in gravitational physics,we study the correction of black hole thermodynamic entropy in the framework of GBD theory.In this thesis we calculate the contribution of the correction term to entropy.It is found that for the smaller values of event horizon radius_（10）r,the effect from correction term to entropy is very obvious,while for the larger values ofr_（10）,the effect of the correction term can be almost ignored.Finally,the dependence of black hole mass,temperature and heat capacity on the event horizon radius in GBD theory is also discussed.