2020/08/31 by Kai Shi, Xuan Wang, Yihong Xiu +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Boundary (topology) #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Covariant transformation #Einstein #Geometric Analysis and Curvature Flows #Hamiltonian (control theory) #History and Theory of Mathematics #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Phase space #Physics #Quantum mechanics #Relativity and Gravitational Theory #Submanifold #hep-th
paper · pdf · doi:10.1088/1572-9494/ac2a1b
version to appear in Communications in Theoretical Physics
arxiv created 2021/09/26 · openalex publication_date 2021/09/26 · arxiv updated 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find for Einstein's gravity that the variational principle works only in its submanifold with the null boundaries given by the expansion-free and shear-free hypersurfaces rather than in the whole covariant phase space. This implies that the key requirement in Harlow–Wu's algorithm for the timelike boundaries is too restrictive for the null ones. To incorporate more generic situations into Harlow–Wu's algorithm, we relax such a requirement. As a result, we successfully reproduce the Hamiltonian obtained previously by Wald–Zoupas’ prescription for Einstein's gravity.