Black Hole Solutions And Their Thermodynamics And Dynamics

A black hole,predicted by the theory of General Relativity(GR),is an exotic celestial body.In recent years,both the large number of binary black hole merger events detected via the Gravitational Waves(GWs)and the black hole photo taken by the Event Horizon Telescope indirectly conformed the existence of black holes to a very significant extent.Simultaneously,the precision of data has confirmed the validity of GR.However,these observations cannot eliminate the possibility of modified gravities,which can solve the problems that GR cannot explain,for example the late time accelerated expansion and the inflation in early times.I first studied the dynamical and thermodynamical properties of black holes in General Relativity,including the Quasi-Normal Modes(QNMs),thermodynamical phase transition,photon orbits and the Strong Cosmic Censorship(SCC).Intriguingly,when a black hole approaches its extremal state,i.e.the internal horizon and the external horizon of the black hole coincide,these seemingly irrelevant properties become closely connected with each other.When we investigated the QNMs and the thermodynamical phase transition of the charged BTZ black holes,we found that with the black hole approaching its extremal state,i.e.the second order phase transition point of these black holes,the imaginary parts of the QNMs approach zero.It describes that the scalar perturbation in near-extremal black hole spacetime would last quite a long time,while in exactly extremal black hole spacetime the perturbation will not decay,even may enhance,indicating the dynamical instability of the extremal black hole spacetimes.This correspondence still holds well even with nonlinear electromagnetic field,which means that QNMs can serve as a sensitive probe of the phase transition.Besides,we analysed several kinds of extremal black holes in Anti-de Sitter(Ad S)spacetimes,and found that a large class of extremal Ad S black holes admits stable photon orbits on their event horizon.We also discussed two kinds of possible instability triggered by the photon orbits.Recent years,the mathematical relation between the SCC and QNMs has been found.After that the study on the violation of the SCC for near extremal charged black holes becomes a hot topic.We generalized the study to higher-dimensional charged black holes and discussed the influence on the violation of SCC.Later on,I extended my research area to modified theories of gravity,studying the black hole solutions and the scalarization of black holes in modified gravities.The black hole solutions in modified gravities have similar or different properties with the black hole solutions in GR,these properties can help us distinguish different modified theories and give the constraints.In non-minimal coupling theory,we obtained a general black hole solution with arbitrary coupling constant,and discuss analytically the possibility of de Sitter(d S)black holes.In 1)()theory,we obtained exact charged black hole solutions in -dimensions which reveal some novel properties when compared to GR solutions,then we studied their thermodynamics.Also in 1)()gravity,we checked the possibility of scalarization of GR solutions.We found that instead of the direct coupling between matter and gravity,only the nonlinearity of 1)()gravity can lead to curvature scalarization.Finally we proposed a new class of higher-derivative modified gravity,Gauss-Bonnet extended Starobinsky model,and studied the spontaneous scalarization of GR solutions in this theory.