## On Clifford Space and Higher Curvature Gravity

**Authors:** Carlos Castro

Clifford-space Gravity is revisited and new results are found. A derivation of the proper expressions for the connections (with $torsion$) in Clifford spaces ( $C$-spaces) is presented. The introduction of hyper-determinants of hyper-matrices are instrumental in the derivation of the $ C$-space generalized gravitational field equations from a variational principle and based on the extension of the Einstein-Hilbert-Cartan action. We conclude by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan higher curvature gravity with torsion and extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions. Introducing nonmetricity furnishes higher curvature extensions of metric affine theories of gravity.

**Comments:** 16 Pages. submitted to Foundations of Physics

**Download:** **PDF**

### Submission history

[v1] 2012-06-28 01:24:05

**Unique-IP document downloads:** 103 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*