Reloading Black Hole Thermodynamics with Noether Charges

• Vahid Taghiloo (Institute for Advanced Studies in Basic Sciences (IASBS) & IPM)

In electromagnetism, the Gauss law and in gravity, Komar integrals, both yield conserved quantities like electric charge and energy-momentum as "surface" integrals, contrasting with the more familiar volume integrals associated with the usual global conserved charges. The inherently lower-dimensional nature of conserved charges in theories with local symmetries allows us to consider the radial (spatial) conservation/balance equation, in addition to the standard temporal conservation law. In this talk, I will demonstrate how the Samrr relation and the black hole first law naturally emerge from the radial conservation of Noether charges and their variations. Finally, we will explore the origin of non-covariance in gravitational charges and its implications.