Lanczos-Lovelock and f(R) Gravity from Clifford Space Geometry
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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.
KeywordsClifford algebras Lanczos-Lovelock gravity f(R) gravity Extended theories of gravity
We are indebted to M. Bowers for assistance.
- 4.Hestenes, D.: Spacetime Algebra. Gordon and Breach, New York (1996) Google Scholar
- 8.Baylis, W.: Electrodynamics, A Modern Geometric Approach, Boston. Birkhäuser, Basel (1999) Google Scholar
- 12.Kastor, D.: The Riemann-Lovelock curvature tensor. arXiv:1202.5287
- 13.Dadhich, N., Jhingan, S.: The Lovelock gravity in the critical spacetime dimension. arXiv:1205.4575
- 14.Sisman, T., Gullu, I., Tekin, B.: Spectra, vacua and the unitarity of Lovelock gravity in D-dimensional AdS spacetimes. arXiv:1204.3814
- 15.Kastor, D., Mann, R.: On Black strings and branes in Lovelock gravity. hep-th/0603168
- 17.Cayley, A.: Cambr. Math. J. 4, 193 (1845) Google Scholar
- 19.Capozziello, S., De Laurentis, M.: Extended theories of gravity. Phys. Rep. (to appear). arXiv:1108.6266
- 21.Castro, C.: Progress in Clifford Space Gravity. Adv. Appl. Clifford Alg. (submitted) (submitted) Google Scholar