Noether Charges, Brown-York Quasilocal Energy and Related Topics

Abstract

The Lagrangian proposed by York et al. and the covariant first order Lagrangian for General Relativity are introduced to deal with the (vacuum) gravitational field on a reference background. The two Lagrangians are compared and we show that the first one can be obtained from the latter under suitable hypotheses. The induced variational principles are also compared and discussed. A conditioned correspondence among Noether conserved quantities, quasilocal energy and the standard Hamiltonian obtained by 3+1 decomposition is also established. As a result, it turns out that the covariant first order Lagrangian is better suited whenever a reference background field has to be taken into account, as it is commonly accepted when dealing with conserved quantities in non-asymptotically flat spacetimes. As a further advantage of the use of a covariant first order Lagrangian, we show that all the quantities computed are manifestly covariant, as it is appropriate in General Relativity.

43 pages, 3 figures, PlainTeX file

References in corpus (4)

• Relativistic conservation laws and integral constraints for large cosmological perturbations
• Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting
• Remarks on Noether charges and black holes entropy
• Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

Cited by in corpus (21)

• Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes
• Quasilocal Thermodynamics of Kerr and Kerr-anti-de Sitter Spacetimes and the AdS/CFT Correspondence
• A covariant formalism for Chern-Simons gravity
• Approximate Noether Symmetries of the Geodesic Equations for the Charged-Kerr Spacetime and Rescaling of Energy
• Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
• Mass, Action and Entropy of Taub-Bolt-dS Spacetimes
• ADM Pseudotensors, Conserved Quantities and Covariant Conservation Laws in General Relativity
• Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
• Hamiltonian, Energy and Entropy in General Relativity with Non-Orthogonal Boundaries
• Covariant canonical formulations of classical field theories
• Boundary conditions from boundary terms, Noether charges and the trace K lagrangian in general relativity
• Boundary conditions in first order gravity: Hamiltonian and Ensemble
• Noether currents and charges for Maxwell-like Lagrangians
• Conformal gravity: light deflection revisited and the galactic rotation curve failure
• The relative energy of homogeneous and isotropic universes from variational principles
• Off-shell Noether currents and potentials for first-order general relativity
• Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)
• Thin-shell wormholes in 2+1-dimensional Einstein-Scalar Theory
• The entropy of Taub-Bolt-AdS from an improved action principle
• Energy and Hamiltonian in first order gravity
• Emergent Gravity from an Augmented Variational Principle