Gravitational Physics at Boundaries: Horizon Symmetries, Entropy and Flux

The presence of boundaries in a spacetime region can have important consequences for gravitational dynamics, giving rise to non-trivial symmetries, charges and fluxes. In this talk, I will discuss these aspects in two closely related settings: isolated horizons as inner boundaries and asymptotic boundaries with codimension-2 corners . Using the weak isolated horizon framework, I will first discuss how the algebra of residual horizon symmetries leads to an equidistant spectrum of the horizon area operator in gravity non-minimally coupled to a scalar field. This equidistant spectrum gives rise to the black hole entropy along with its corrections. I will then discuss the charge associated with residual local Lorentz boosts at the horizon. For the Lovelock class of theories, this charge turns out to be exactly the Wald entropy. Finally, I will consider spacetime regions with non-smooth boundaries, where different boundary components meet at codimension-two surfaces and give rise to additional terms in the gravitational action. I will discuss how these terms enter the covariant phase space and how they may affect gravitational flux and the corresponding flux-balance laws.