Abstract
The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. As an example we analyze S3 equipped with a contact structure together with an associated metric tensor such that the canonical generators of the contact distribution are null. The resulting Lorentzian metric is shown to be a vacuum solution of three-dimensional massive gravity. Moreover, by coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. Finally, we repeat the exercise for the Abelian Higgs theory.
Highlights
There is a long tradition on applications of geometrical methods in physics; over the years branches as Hamiltonian dynamics, geometric optics, fluid dynamics and General Relativity have benefited from the techniques developed with a geometric perspective [1,2,3,4,5,6]
In this letter we show that such relations are completely captured by the geometry of a class of three dimensional metric contact manifolds whose structural elements give rise to propagating force-free fields
We study the case of S3 endowed with a contact structure together with an associated metric such that the generators of the contact distribution together with the Reeb vector field generate a null triad for a
Summary
Daniel Flores-Alfonso∗ and Marco Maceda† Departamento de Fısica, Universidad Autonoma Metropolitana - Iztapalapa, Avenida San Rafael Atlixco 186, A.P. 55534, C.P. 09340, Ciudad de Mexico, Mexico. Lopez-Monsalvo‡ Conacyt-Universidad Autonoma Metropolitana Azcapotzalco, Avenida San Pablo Xalpa 180, Azcapotzalco, Reynosa Tamaulipas, C.P. 02200, Ciudad de Mexico, Mexico. The defining property of every three-dimensional ε-contact manifold is shown to be equivalent to requiring the fulfillment of London’s equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold that is K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity. By coupling the New Massive Gravity action to Maxwell-Chern-Simons we obtain a class of charged solutions stemming directly from the para-contact metric structure. PACS numbers: 04.60.Kz, 11.10.Kk, 11.15.Wx Keywords: Contact geometry, New Massive Gravity arXiv:2011.13499v3 [gr-qc] 22 Feb 2021
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