arXiv subjects

K. V. S. Araújo

Publications and source records attributed to K. V. S. Araújo.

3 recordsLinked to original sources

arXiv2026

On a Gödel-like Solution in Non-Relativistic Gravity

The article deals with Gödel-like solutions in the context of Galilean gravity, a geometric formulation of non-relativistic gravitation defined on a five-dimensional Galilean manifold. Within this framework, non-relativistic matter fields admit a covariant description, while the physical Newtonian dynamics is recovered through an immersion into the usual $3+1$ spacetime. By adopting a Gödel-like metric ansatz and coupling the gravitational field to a Galilean fluid derived from a variational principle, we obtain a system of highly nonlinear and coupled field equations. Exact solutions are constructed by fixing the matter sector consistently with the field equations. The resulting configurations describe rotating non-relativistic universes and satisfy $D(x)>H(x)$ throughout the entire spatial domain. As a consequence, the associated Killing vector remains spacelike everywhere and no closed timelike curves arise.

gr-qc↗

arXiv2025

On Nonrelativistic Isotropic and Homogeneous Universe

This article deals with a nonrelativistic cosmological model based on Galilean covariance, formulated within a five-dimensional Galilean manifold. Within this framework, we construct an isotropic and homogeneous metric analogous to the Friedmann--Robertson--Walker metric but without a universal speed limit. Two distinct solutions of the Einstein-like field equations are obtained: (i) a vacuum configuration ($λ=0$) yielding an exponential--quadratic scale factor, and (ii) a dust-dominated universe ($λ=1$) described by a non-interacting nonrelativistic fluid. Upon dimensional reduction to $3+1$ spacetime through a specific embedding, the model naturally develops anisotropy in the scale factor and density, consistent with the near-zero spatial curvature inferred from Planck data. In the case of vanishing spatial curvature, the framework reproduces Milne's Newtonian cosmology because this condition leads to a vanishing pressure. This provides an independent nonrelativistic setting for cosmological dynamics within Galilean covariance.

gr-qc↗

arXiv2021

The Landau Problem and non-Classicality

Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a de Sitter space-time in five dimensions. A Hilbert space is constructed, endowed with a symplectic structure, which is used as a representation space for the Lie algebra of G. This representation gives rise to the spin-zero Schrödinger (Klein-Gordon-like) equation for the wave functions in phase space, such that the dependent variables have the content of position and linear momentum. This is a particular example of a conformal theory, such that the wave functions are associated with the Wigner function through the Moyal product. We construct the Pauli-Schrödinger (Dirac-like) equation in phase space in its explicitly covariant form. In addition, we analyze the gauge symmetry for spin 1/2 particles in phase space and show how to implement the minimal coupling in this case. We applied to the problem of an electron in an external field, and we recovered the non-relativistic Landau Levels. Finally, we study the parameter of negativity associated with the non-classicality of the system.

hep-th↗