The universal 'energy' operator
arXiv:gr-qc/0608065 · doi:10.1088/0264-9381/23/23/N01
Abstract
The "positive square" of any tensor is presented in a universal and unified manner, valid in Lorentzian manifolds of arbitrary dimension, and independently of any (anti)-symmetry properties of the tensor. For rank-m tensors, the positive square has rank 2m. Positive here means future, that is to say, satisfying the dominant property. The standard energy-momentum and super-energy tensors are recovered as appropriate parts of the general square. A richer structure of principal null directions arises.
13 pages, no figures; minor improvements and corrections. This is a larger, expanded version, containing proofs and explanations not available in the short Note to be published in CQG
References in corpus (13)
- Super-energy tensors
- Causal structures and causal boundaries
- Null cone preserving maps, causal tensors and algebraic Rainich theory
- General Electric-Magnetic decomposition of fields, positivity and Rainich-like conditions
- General study and basic properties of causal symmetries
- On the Causal Propagation of Fields
- Remarks on Superenergy Tensors
- Symmetric hyperbolic systems for Bianchi equations
- Positivity and conservation of superenergy tensors
- Causal symmetries
- A weighted de Rham operator acting on arbitrary tensor fields and their local potentials
- Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
- Superenergy tensors for a massive scalar field
Cited by in corpus (6)
- Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
- Moeller's Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane
- Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
- Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor
- Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-singular Black Hole Space-time Geometry
- Algebraic classification of the gravitational field in general metric-affine geometries