Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-11-27
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
to be published in "Classical and Quantum Gravity Research Progress", Nova Science Publishers, Inc
Scientific paper
The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Maxwell-like system of equations. In the framework of the coframe geometry construction, we propose a geometrical action for the coframe gravity. It is similar to the Einstein-Hilbert action of GR, but the scalar curvature is constructed from the general coframe connection. We show that this geometric Lagrangian is equivalent to the coframe Lagrangian up to a total derivative term. Moreover there is a family of coframe connections which Lagrangian does not include the higher order terms at all. In this case, the equivalence is complete.
of Jerusalem Hebrew University
of Mathematics Yakov Itin (Institute
of Technology Jerusalem College
No associations
LandOfFree
Coframe geometry and gravity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Coframe geometry and gravity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coframe geometry and gravity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-686350