Averaging geometrical objects on a differentiable manifold
arXiv:1003.2014 · doi:10.1142/S0218271810018062
Abstract
We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenböck connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold.
References in corpus (6)
- The universe seen at different scales
- On cosmological observables in a swiss-cheese universe
- Averaging in Spherically Symmetric Cosmology
- Averaging Spherically Symmetric Spacetimes in General Relativity
- A Complete Cosmological Solution to the Averaged Einstein Field Equations as found in Macroscopic Gravity
- Spherically Symmetric Solutions in Macroscopic Gravity
Cited by in corpus (12)
- Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
- Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology
- What is dust? - Physical foundations of the averaging problem in cosmology
- Evolution of a periodic eight-black-hole lattice in numerical relativity
- Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence
- Averaging in cosmological models using scalars
- Backreaction: Gauge and Frame Dependences
- Expansion and Growth of Structure Observables in a Macroscopic Gravity Averaged Universe
- Averaging in cosmology based on Cartan scalars
- Averaging in LRS class II spacetimes
- Unimodular Gravity and Averaging
- An Almost-FLRW Universe as the Averaged Geometry in Macroscopic Gravity