Quasi-local Hamiltonian for generalized Kerr-Schild black holes in the Iyer-Wald formalism

Abstract

Grounded in the covariant phase space approach of the Iyer-Wald formalism, we propose a quasi-local Hamiltonian for generalized Kerr-Schild (GKS) black holes. Evaluated for spherically symmetric spacetimes over a flat Minkowski background, our formulation recovers the Misner-Sharp mass. Because this framework relies solely on the GKS structure, it provides a straightforward extension of the Misner-Sharp mass to rotating geometries. We further extend our analysis to asymptotically anti-de Sitter (AdS) black holes, where a renormalization procedure to subtract the background AdS energy naturally emerges. By employing this technique, we establish a geometric quasi-local formulation of Kerr-AdS thermodynamics.