On the compatibility of Lorentz-metrics with linear connections on 4-dimensional manifolds

Abstract

This paper considers 4-dimensional manifolds upon which there is a Lorentz metric, h, and a symmetric connection and which are originally assumed unrelated. It then derives sufficient conditions on the metric and connection (expressed through the curvature tensor) for the connection to be the Levi-Civita connection of some (local) Lorentz metric, g, and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

arXiv commentLaTex2e, 19 pages, uses iop style files

References in corpus (2)

• Holonomy groups and spacetimes
• Holonomy and projective symmetry in space-times

Cited by in corpus (3)

• Metric-affine f(R) theories of gravity
• The principle of equivalence and projective structure in space-times
• Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds