## Services on Demand

## Journal

## Article

## Indicators

- Cited by SciELO
- Access statistics

## Related links

- Similars in SciELO

## Share

## Revista mexicana de física

*Print version* ISSN 0035-001X

#### Abstract

NIETO, J.A. and LEON, E.A.. **Higher dimensional gravity and Farkas property in oriented matroid theory**.* Rev. mex. fis.* [online]. 2012, vol.58, n.2, pp.133-138.
ISSN 0035-001X.

We assume gravity in a *d*-dimensional manifold *M *and consider a splitting of the form *M = M _{p} *×

*M*, with

_{q}*d = p*+

*q*. The most general two-block metric associated with

*M*and

_{p}*M*is used to derive the corresponding Einstein-Hilbert action

_{q}*S*. We focus on the special case of two distinct conformal factors

*ψ*and

*φ*(

*ψ*for the metric in

*M*and

_{p}*φ*for the metric in

*M*), and we write the action

_{q}*S*in the form

*S = S*, where

_{p}+S_{q}*S*and

_{p}*S*are actions associated with

_{q}*M*and

_{p}*M*, respectively. We show that a simplified action is obtained precisely when

_{q}*ip = p*. In this case, we find that under the duality transformation

^{-1}*φ*↔

*φ*

^{-1}, the action

*S*for the M

_{p}_{p}-space or the action

*S*for the

_{q}*M*-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.

_{q}**Keywords
:
**Higher dimensional gravity; gravitational duality; 2t physics.