Improved Energy-Momentum Currents in Metric-Affine Spacetime

Abstract

In Minkowski spacetime it is well-known that the canonical energy-momentum current is involved in the construction of the globally conserved currents of energy-momentum and total angular momentum. For the construction of conserved currents corresponding to (approximate) scale and proper conformal symmetries, however, an improved energy-momentum current is needed. By extending the Minkowskian framework to a genuine metric-affine spacetime, we find that the affine Noether identities and the conformal Killing equations enforce this improvement in a rather natural way. So far, no gravitational dynamics is involved in our construction. The resulting dilation and proper conformal currents are conserved provided the trace of the energy-momentum current satisfies a (mild) scaling relation or even vanishes.

14pp

References in corpus (1)

• Cosmology and the Fate of Dilatation Symmetry

Cited by in corpus (16)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Black Holes with Weyl Charge and Non-Riemannian Waves
• Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry
• Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
• Torsion waves in metric-affine field theory
• Towards complete integrability of two dimensional Poincaré gauge gravity
• Symmetry and Equivalence in Teleparallel Gravity
• Avoiding degenerate coframes in an affine gauge approach to quantum gravity
• Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetries
• Invariant conserved currents for gravity
• Invariant conserved currents in generalized gravity
• Teleparallel Geometry with a Single Affine Symmetry
• Teleparallel Geometry with Spherical Symmetry: The diagonal and proper frames
• Symmetries and conserved quantities with arbitrary torsion: A generalization of Killing's theorem
• On the geometric origin of the energy-momentum tensor improvement terms
• On the Energy-Momentum and Spin Tensors in the Riemann-Cartan Space