Off-Shell ADT Conserved Quantities in Palatini Gravity

Abstract

In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein-Hilbert action, the most general $L(g_{\mu \nu },R^{\lambda }{}_{\nu \alpha \mu },T^{\lambda }{}_{\alpha \beta },Q_{\alpha \mu \nu })$ theories and the teleparallel Palatini gravity.

arXiv comment20 pages, version to be published in Class. Quantum Grav

References in corpus (42)

• Black Hole Entropy is Noether Charge
• The Dynamics of General Relativity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Energy in Generic Higher Curvature Gravity Theories
• Gravitational Energy in Quadratic Curvature Gravities
• Surface charge algebra in gauge theories and thermodynamic integrability
• Teleparallel Palatini theories
• Black hole mass and angular momentum in topologically massive gravity
• On the covariance of teleparallel gravity theories
• Boundary charges in gauge theories: using Stokes theorem in the bulk
• Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
• Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories
• Quasilocal quantities for GR and other gravity theories
• Quasi-Local Conserved Charges in Covariant Theory of Gravity
• Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
• Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries
• Generalized Smarr relation for Kerr AdS black holes from improved surface integrals
• Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry
• Noether Charge and Black Hole Entropy in Modified Theories of Gravity
• Quasilocal Energy-Momentum for Geometric Gravity Theories
• Gravitational Energy for GR and Poincare Gauge Theories: a Covariant Hamiltonian Approach
• Energy and Angular Momentum in Generic F(Riemann) Theories
• The Hamiltonian boundary term and quasi-local energy flux
• Spacetime thermodynamics in the presence of torsion
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Noether charge and black hole entropy in teleparallel gravity
• Conserved Charges in Extended Theories of Gravity
• Quasi-local conserved charges and holography
• Conserved Charges and First Law of Thermodynamics for Kerr-de Sitter Black Holes
• Revisiting Conserved Charges in Higher Curvature Gravitational Theories
• Negative Mass Solitons in Gravity
• Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries
• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Stress-Energy-Momentum of Affine-Metric Gravity. Generalized Komar Superportential
• Noether Current, Black Hole Entropy and Spacetime Torsion
• Invariant conserved currents in generalized gravity
• Conserved currents in the Palatini formulation of general relativity
• Energy-Momentum and Gauge Conservation Laws
• Generalized Off-Shell ADT Conserved Charges in the Presence of Matter Chern-Simons Term