International Journal of Theoretical Physics

, Volume 52, Issue 1, pp 28–41 | Cite as

Lanczos-Lovelock and f(R) Gravity from Clifford Space Geometry

  • 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 generalized connections in Clifford spaces (C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity 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 μν ),… actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D>4 play an important role in finding specific examples.


Clifford algebras Lanczos-Lovelock gravity f(R) gravity Extended theories of gravity 



We are indebted to M. Bowers for assistance.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Center for Theoretical Studies of Physical SystemsClark Atlanta UniversityAtlantaUSA

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