Higher dimensional gravity and Farkas property in oriented matroid theory

• Autores: J. A. Nieto, E.A. León
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 58, Nº. 2, 2012, págs. 133-138
• Idioma: inglés
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• Resumen

  • We assume gravity in a d-dimensional manifold M and consider a splitting of the form M = M_(p) x M_(q) with d = p + q. The most general two-block metric associated with M_(p) and M_(q) is used to derive the corresponding Einstein-Hilber action S. We focus on the special case of two distinct conformal factors "letter psi" and "letter phi" ("letter psi" for the metric en M_(p) and "letter phi" for the metric in M_(q)), and we write the action S in the form S = S_(p) + S_(q), where S_(p) and S_(q) are actions associated with M_(p) and M_(q), respectively. We show that a simplified action is obtained precisely when "letter psi" = "letter phi"^(-1). In this case, we find that under the duality transformation "letter phi" (bidirection) "letter phi"^(-1), the action S_(p) for the M_(p)-space or the action S_(q) for the M_(q)-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.