Volume 11, Issue Supplement 1, October 2004, Pages 204 - 216
Quadratic non-Riemannian Gravity
Available Online 1 October 2004.
- https://doi.org/10.2991/jnmp.2004.11.s1.28How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - Dmitri Vassiliev PY - 2004 DA - 2004/10 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 - https://doi.org/10.2991/jnmp.2004.11.s1.28 ID - Vassiliev2004 ER -