2010/03/21 by R. J. van den Hoogen, Hoogen, R. J. van den
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.1003.4020
10 pages; To appear in the Proceedings of the 12th Marcel Grossman Meeting; A new reference added and some small editorial changes made in V2.
openalex publication_date 2010/03/21 · arxiv created 2010/04/15 · arxiv updated 2010/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining a mathematically precise covariant averaging procedure for tensor fields over differentiable manifolds. Together, these two ideas have been called the averaging problem for General Relativity. In the first part of the talk, an attempt to review some the various approaches to this problem will be given, highlighting strengths, weaknesses, and commonalities between them. In the second part of the talk, an argument will be made, that if one wishes to develop a well-defined averaging procedure, one may choose to parallel transport along geodesics with respect to the Levi-Cevita connection or, use the Weitzenböck connection and ensure the transportation is independent of path. The talk concludes with some open questions to generate further discussion.