Numerical Study Of Charged AdS Spacetime

Since the propose of general relativity,finding the solutions of Einstein equations is al-ways the most important question in theoretical physics or even in mathematics.Due to the nonlinearity of Einstein equations,it is hard to find analytical solutions.Numerical relativity provides a useful way for finding solutions and has found wide applicability in the context of gravitational high energy physics,especially in the holographic duality.One important problem related to solutions of Einstein equations is singularity.The weak cosmic censorship conjec-ture(WCCC)states that the singularity must be hidden in event horizon and can not be observed from future null infinity.Although the concrete proof for the validity of WCCC has not been es-tablished,there exist lots of works of testing the validity of WCCC.Recently,G.T.Horowitz et al.propose that there might be relations between WCCC and weak gravity conjecture(WGC).We will introduce this work and make some generalizations.We will also give a new family of charged Anti de Sitter(AdS)black hole solutions with deformed horizon.Firstly,we introduce the background,including weak cosmic censorship and weak gravity conjecture.Considering all works in Sec.2 and Sec.3 are based on AdS spacetime represent-ed by Poincare coordinates,we introduce Einstein equations with cosmological constant and the metric in AdS spacetime in detail.Then we give an introduction of AdS black hole solu-tions.In Sec.2,with studying the near external charged AdS black hole,we give the weak gravity conjecture bound of charge-to-mass in AdS spacetime.Then we introduce a class of counterexample of WCCC and the relations between this class of counterexample and WGC.In Sec.3,we generalize this class of counterexample to non-liner electrodynamic.Con-sidering Einstein-Born-Infeld action in four dimensional AdS spacetime,we numerically solve coupled equations of motion and calculate the Kretschmann curvature to prove the existence of singularity.Then we introduce charged scalar field to the model and calculate Kretschmann curvature and minimal value of charge in detail.We find that this class of counterexample to cosmic censorship would be removed if the charge of scalar field is above the bound of charge,which provids a kind of possibility of WGC in Born-Infeld electrodynamic.In Sec.4,we introduce another family of AdS black hole solutions.Adding differential rotation boundary in conformal boundary,we obtain deforming charged AdS black hole solu-tions and study horizon geometry,entropy and stability of black holes.Due to the existence of charge q,the phase diagram of entropy is more complicated.We consider two cases of solu-tions:(1)fixing the chemical potential μ;(2)changing the value of μ according to the values of horizon radius and charge.In the first case,it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature,but these two black holes have same horizon geometry and entropy.However,this kind of solutions can not reduce to standard RN-AdS black hole.The second case ensures that the deforming charged AdS black hole solutions can reduce to standard RN-AdS black holes.