Charges in general relativity and black hole thermodynamics

We shed a new light on the long-standing problem of covariant charges in diffeomorphism invariant theories such as general relativity by noting the other important feature of the theory, the background independence. To this end, we develop covariant phase space formalism in which we allow for the boundaries of spacetime to have arbitrary fluctuations. Within this formalism we show noncovariance of charges appear in inevitable integration constants that also break background independence in the expression of charges. We then apply the same formalism to black hole thermodynamics. We generalize the seminal Iyer-Wald derivation the first law of black hole thermodynamics by relaxing the need for the assumptions at a bifurcation surface and asymptotic infinity, as well as addressing questions regarding the integrability of charges. We also present a first principles derivation of the Smarr relation within our framework.