2016/10/19 by Ezequiel F. Boero, Osvaldo M. Moreschi, Boero, Ezequiel F. +1
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1610.06040
openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a definition of tensor fields which are average of tensors over a manifold, with a straightforward and natural definition of derivative for the averaged fields; which in turn makes a suitable and practical construction for the study of averages of tensor fields that satisfy differential equations. Although we have in mind applications to general relativity, our presentation is applicable to a general n-dimensional manifold. The definition is based on the integration of scalars constructed from a physically motivated basis, making use of the least amount of geometrical structure. We also present definitions of covariant derivative of the averaged tensors and Lie derivative.