## Progress in Clifford Space Gravity

**Authors:** Carlos Castro

Clifford-space Gravity is revisited and new results are found.
The Clifford space ($ C$-space) generalized gravitational field equations are obtained from a variational principle and which is based on an extension of the Einstein-Hilbert-Cartan action. One of the main results of this work is that the $C$-space connection requires torsion in order to have consistency between the Clifford algebraic structure and the zero nonmetricity condition $ \nabla_K g^{MN} = 0 $. A discussion on the cosmological constant and bi-metric theories of gravity follows. We continue by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan (LLC) higher curvature gravity with torsion. We finalize by pointing out that $ C$-space gravity involves higher-spins beyond spin $ 2 $ and argue why one could view the LLC higher curvature actions, and
other extended gravitational theories based on $ f ( R ), f ( R_{\mu \nu} ), ... $ actions, for polynomial-valued functions, as mere $effective$ actions after integrating the $C$-space gravitational action with respect to all the poly-coordinates, except the vectorial ones $ x^\mu$.

**Comments:** 22 Pages. Submitted to Advances in Applied Clifford Algebras

**Download:** **PDF**

### Submission history

[v1] 2012-07-24 09:18:58

[v2] 2012-07-25 03:48:47

**Unique-IP document downloads:** 95 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.*

*
*