2008/09/30 by Roh-Suan Tung, Hoi-Lai Yu
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Diffeomorphism #Hamiltonian (control theory) #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Spacetime #Symplectic geometry #gr-qc
paper · pdf · doi:10.1103/physrevd.78.104010
published as Phys.Rev.D78:104010,2008 · 8 pages, added appendix, version to appear in Phys. Rev. D
arxiv created 2008/10/16 · openalex publication_date 2008/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A general expression for quasilocal energy flux for spacetime perturbation is derived from covariant Hamiltonian formulation using functional differentiability and symplectic structure invariance, which is independent of the choice of the canonical variables and the possible boundary terms one initially puts into the Lagrangian in the diffeomorphism invariant theories. The energy flux expression depends on a displacement vector field and the 2-surface under consideration. We apply and test the expression in Vaidya spacetime. At null infinity the expression leads to the Bondi type energy flux obtained by Lindquist, Schwartz, and Misner. On dynamical horizons with a particular choice of the displacement vector, it gives the area balance law obtained by Ashtekar and Krishnan.