Dept Math & Stat UiT, Forskningsparken B459
  8 Dec 2021 Wed 10:00-11:00

David Duncan McNutt (University of Stavanger)

When can a teleparallel geometry be classified by its scalar polynomial torsion invariants

General Relativity (GR) is formulated using Lorentzian manifolds with a connection which is required to be metric-compatible and the resulting torsion tensor vanishes. Interestingly, GR can be reformulated on Lorentzian manifolds with a different connection which is still metric-compatible but now the curvature tensor must vanish. This alternative gravity theory is known as the teleparallel equivalent of general relativity (TEGR) and any geometry with this choice of connection will be called a teleparallel geometry.

For a given solution of GR, it is possible to generate a corresponding solution of TEGR, however, this approach is not one-to-one, and we can generate many inequivalent solutions of TEGR. To determine if two solutions of TEGR are equivalent, we could compare their respective scalar polynomial torsion invariants. However, it is expected that the set of all scalar polynomial torsion invariants will not uniquely characterize all teleparallel geometries, so it would be helpful to know when we can use these torsion invariants. In this talk I will discuss the problem in four dimensions and introduce the class of teleparallel geometries which are not characterized by their scalar polynomial torsion invariants.