Quadratic non-Riemannian Gravity

DOI

10.2991/jnmp.2004.11.s1.28How to use a DOI?

Abstract

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler­Lagrange equations. In the first part of the paper we look for Riemannian solutions, i.e. solutions whose connection is Levi-Civita. We find two classes of Rimannian solutions: 1) Einstein spaces, and 2) spacetimes with metric of a pp-wave and parallel Ricci curvature. We prove that for a generic quadratic action these are the only Riemannian solutions. In the second part we look for non-Riemannian soltions. We define the notion of a "Weyl pseudoinstanton" (metric compatible spacetime whose curvature is purely Weyl) and prove that a Weyl pseudoinstanton is a solution of our field equations. Using the pseudoinstanton approach we construct explicitly a non-Riemannian solution which is a wave of torsion in Minkowski space.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Dmitri Vassiliev
PY  - 2004
DA  - 2004/10/01
TI  - Quadratic non-Riemannian Gravity
JO  - Journal of Nonlinear Mathematical Physics
SP  - 204
EP  - 216
VL  - 11
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.s1.28
DO  - 10.2991/jnmp.2004.11.s1.28
ID  - Vassiliev2004
ER  -