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Revista mexicana de física

Print version ISSN 0035-001X

Rev. mex. fis. vol.58 n.2 México Apr. 2012




Higher dimensional gravity and Farkas property in oriented matroid theory


J.A. Nieto and E.A. León


Facultad de Ciencias Físico–Matemáticas de la Universidad Autónoma de Sinaloa, 80010, Culiacán Sinaloa, México, e–mails:;


Recibido el 17 de octubre de 2011.
Aceptado el 16 de febrero de 2012.



We assume gravity in a d–dimensional manifold M and consider a splitting of the form M = Mp × Mq, with d = p + q. The most general two–block metric associated with Mp and Mq is used to derive the corresponding Einstein–Hilbert action S. We focus on the special case of two distinct conformal factors ψ and φ (ψ for the metric in Mp and φ for the metric in Mq), and we write the action S in the form S = Sp+Sq, where Sp and Sq are actions associated with Mp and Mq, respectively. We show that a simplified action is obtained precisely when ip = p–1. In this case, we find that under the duality transformation φ φ–1, the action Sp for the Mp–space or the action Sq for the Mq–space remain invariant, but not both. This result establishes an analogy between Farkas property in oriented matroid theory and duality in general relativity. Furthermore, we argue that our approach can be used in several physical scenarios such as 2t physics and cosmology.

Keywords: Higher dimensional gravity; gravitational duality; 2t physics.


PACS: 04.60.–m; 04.65.+e; 11.15.–q; 11.30.Ly





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