arXiv subjects

E. A. Leon

Publications and source records attributed to E. A. Leon.

6 recordsLinked to original sources

arXiv2013

SL(2,R)-geometric phase space and (2+2)-dimensions

We propose an alternative geometric mathematical structure for arbitrary phase space. The main guide in our approach is the hidden SL(2,R)-symmetry which acts on the phase space changing coordinates by momenta and vice versa. We show that the SL(2,R)-symmetry is implicit in any symplectic structure. We also prove that in any sensible physical theory based on the SL(2,R)-symmetry the signature of the flat target "spacetime" must be associated with either one-time and one-space or at least two-time and two-space coordinates. We discuss the consequences as well as possible applications of our approach on different physical scenarios.

hep-th↗

arXiv2013

Higher dimensional black holes as constrained systems

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d=4, where the Reissner-Nordström solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries and dynamics of black holes, as well as some quantum aspects.

gr-qc↗

arXiv2011

Higher Dimensional Cosmology: Relations among the radii of two homogeneous spaces

We study a cosmological model in 1+D+d dimensions where D dimensions are associated with the usual Friedman-Robertson-Walker type metric with radio a(t) and d dimensions corresponds to an additional homogeneous space with radio b(t). We make a general analysis of the field equations and then we obtain solutions involving the two cosmological radii, a(t) and b(t). The particular case D=3, d=1 is studied in some detail.

gr-qc↗

arXiv2010

Higher Dimensional Gravity and Farkas Property in Oriented Matroid Theory

We assume gravity in a $d$-dimensional manifold $M$ and consider a splitting of the form $M=M_{p}\times M_{q}$, with $d=p+q$. The most general two-block metric associated with $M_{p}$ and $M_{q}$ is used to derive the corresponding Einstein-Hilbert action $\mathcal{S}$. We focus on the special case of two distinct conformal factors $ψ$ and $ϕ$ ($ψ$ for the metric in $M_{p}$ and $ϕ$ for the metric in $M_{q}$), and we write the action $\mathcal{S}$ in the form $\mathcal{S=S}_{p}\mathcal{+S}%_{q} $, where $\mathcal{S}_{p}$ and $\mathcal{S}_{q}$ are actions associated with $M_{p}$ and $M_{q}$, respectively. We show that a simplified action is obtained precisely when $ψ=ϕ^{-1}$. In this case, we find that under the duality transformation $ϕ\leftrightarrow ϕ^{-1}$, the action $\mathcal{S}_{p}$ for the $M_{p}$-space or the action $\mathcal{S}%_{q}$ 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.

gr-qc↗

arXiv2009

2D Gravity with Torsion, Oriented Matroids and 2+2 Dimensions

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.

hep-th↗

arXiv2009

Issues of duality in Abelian Gauge Theory and in Linearized Gravity

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 type of dualities we explore the possibility of combining them in just one duality formalism.

hep-th↗