Conserved Charges In Gravitational Theory And Their Application To Black Hole Physics

In this thesis we study mainly the application of phase space method of conserved charges(including the covariant phase space method(CPSM)and the solution phase space method(SPSM)),and generalize the formalism for off-shell Abbott-Deser-Tekin(ADT)conserved charges to including matter fields and non-Riemannian geometry.For the application of phase space method,by using the new version of the gedanken experiments proposed by Sorce and Wald,we investigate the weak cosmic censorship conjecture(WCCC)for an Einstein-Maxwell-Dilaton-Axion(EMDA)black hole.Our result shows that the WCCC still holds when the second-order correction of the perturbations is taken into account.As another application of the phase space method,by using the SPSM,we investigate the thermodynamics of black holes in Einstein-aether theory.We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact Einstein-aether black hole solutions.For the off-shell ADT method,we generalize it to including the internal gauge transformation,when the gauge fields are present.For this purpose,we resort to the notion of‘exact symmetry' of SPSM.The generalized off-shell ADT method can be used to compute the conserved charges in the presence of arbitrary matter fields.At the same time,we show that the generalized off-shell ADT formalism is completely equivalent to the phase space method and the Barnich-Brandt-Compère(BBC)formalism.Furthermore,we generalize the off-shell ADT method to the cases of non-Riemannian geometry with torsion and nonmetricity.Our construction is completely based on the general tensoral formaliam.The generalized off-shell ADT method will provide an effective way to compute quasi-local conserved charges.