## Lanczos-Lovelock-Cartan Gravity from Clifford Space Geometry

**Authors:** Carlos Castro

A rigorous construction of Clifford-space Gravity is presented which is compatible with
the Clifford algebraic structure and permits the derivation of the expressions for the connections with $torsion$ in Clifford spaces ( $C$-spaces). The $ C$-space generalized gravitational field equations are derived from a variational principle based on the extension of the Einstein-Hilbert-Cartan action. We continue by arguing how Lanczos-Lovelock-Cartan higher curvature gravity with torsion can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions. In essence, the Lanczcos-Lovelock-Cartan curvature tensors appear as Ricci-like traces of certain components of the $ C$-space curvatures. Torsional gravity is related to higher-order corrections of the bosonic string-effective action. In the torsionless case, black-strings and black-brane metric solutions in higher dimensions $ D > 4 $ play an important role in finding specific examples of solutions to Lanczos-Lovelock gravity.

**Comments:** 23 Pages. submitted to Int. J. Geom. Meth. Mod. Phys.

**Download:** **PDF**

### Submission history

[v1] 2012-06-16 06:34:37

**Unique-IP document downloads:** 177 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.*

*
*