Invariant conserved currents in generalized gravity
arXiv:1507.02191 · doi:10.1103/PhysRevD.92.104010
Abstract
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.
arXiv comment15 pages, RevTex format. arXiv admin note: text overlap with arXiv:1505.01680
References in corpus (45)
- f(R) Theories Of Gravity
- 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
- The motion of point particles in curved spacetime
- Covariant theory of asymptotic symmetries, conservation laws and central charges
- Metric-affine f(R) theories of gravity
- Conserved charges for gravity with locally AdS asymptotics
- Pseudotensors and quasilocal energy-momentum
- 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
- Constraining Torsion with Gravity Probe B
- The dynamics of metric-affine gravity
- Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations
- Level sets of the lapse function in static GR
- On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B
- Motion of spinning test bodies in Kerr spacetime
- Currents and Superpotentials in classical gauge theories: II. Global aspects and the example of Affine gravity
- Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling
- Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry
- Can Gravity Probe B usefully constrain torsion gravity theories?
- Test Matter in a Spacetime with Nonmetricity
- Finally, results from Gravity Probe-B
- Quadratic metric-affine gravity
- Quantum gravity with torsion and non-metricity
- Relativistic Conservation Laws on Curved Backgrounds and the Theory of Cosmological Perturbations
- Probing non-Riemannian spacetime geometry
- Dynamics of test bodies with spin in de Sitter spacetime
- Approximate spacetime symmetries and conservation laws
- Propagation equations for deformable test bodies with microstructure in extended theories of gravity
- Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting
- Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
- Equations of motion in metric-affine gravity: A covariant unified framework
- Conserved Quantities from the Equations of Motion (with applications to natural and gauge natural theories of gravitation)
- Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries
- Quantization and fixed points of non-integrable Weyl theory
- Gravitational energy in stationary spacetimes
- Invariant conserved currents for gravity
- Multipolar test body equations of motion in generalized gravity theories
- Stress-Energy-Momentum of Affine-Metric Gravity. Generalized Komar Superportential
- Improved Energy-Momentum Currents in Metric-Affine Spacetime
- Mass and angular momenta of Kerr anti-de Sitter spacetimes in Einstein-Gauss-Bonnet theory
- Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration
- Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. II. Manifestly Generally Covariant Theories
- Energy-Momentum and Gauge Conservation Laws
Cited by in corpus (12)
- Modified gravity: a unified approach
- Relativistic effects due to gravimagnetic moment of a rotating body
- Noether identities in gravity theories with nondynamical backgrounds and explicit spacetime symmetry breaking
- Spatial curvature in coincident gauge cosmology
- Some globally conserved currents from generalized Killing vectors and scalar test fields
- Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
- A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity
- Conserved currents in the Palatini formulation of general relativity
- Energy, momentum and angular momentum conservations in de Sitter gravity
- Perturbations of the almost Killing equation and their implications
- Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
- Off-Shell ADT Conserved Quantities in Palatini Gravity