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.

We find a link between oriented matroid theory and 2d gravity with torsion. Our considerations may be useful in the context of noncommutative phase space in a target spacetime of signature (2+2) and in a possible theory of gravity ramification.

We start by describing two of the main proposals for duality in abelian gauge theories, namely F(ield strength)-duality approach and the S-duality formalism. We then discuss how F-duality and S-duality can be applied to the case of linearized gravity. By emphasizing the similarities and differences between these two types of dualities we explore the possibility of combining them in just one duality formalism.

Comenzamos describiendo dos propuestas principales de dualidad en teorías abelianas de norma, a saber el enfoque de dualidad-(del campo)F y el formalismo de dualidad-S. De ahí, discutimos como la dualidad-F y la dualidad-S pueden implementarse para el caso de gravedad linealizada. Haciendo énfasis en las similitudes y diferencias entre estos dos tipos de dualidad, exploramos la posibilidad de combinarlos en un sólo formalismo de dualidad.