Remarks on the algebraic structure of (2, 2) double forms
arXiv:2311.14879 · doi:10.1142/S0219887825500537
Abstract
We study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects of these objects. In particular, we focus our attention on the corresponding invariant subspaces and generalise previous relations such as the Ruse-Lanczos identity, the Bel-Matte decomposition and the Lovelock-like quadratic identities. We conclude pointing out some possible applications of the formalism.
References in corpus (15)
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- Super-energy tensors
- Dimensionally Dependent Tensor Identities by Double Antisymmetrisation
- On light propagation in premetric electrodynamics. Covariant dispersion relation
- On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
- Area metric gravity and accelerating cosmology
- Propagation of light in area metric backgrounds
- Geometry of manifolds with area metric: multi-metric backgrounds
- General Electric-Magnetic decomposition of fields, positivity and Rainich-like conditions
- Nonlinear electrodynamics as a symmetric hyperbolic system
- The Kummer tensor density in electrodynamics and in gravity
- On skewon modification of light cone structure
- Old and new results for superenergy tensors from dimensionally dependent tensor identities
- Non-linear electrodynamics non-minimally coupled to gravity:symmetric-hyperbolicity and causal structure
- Light propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws