## 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.

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### Submission history

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

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