The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

Abstract

In this work, we investigate the behaviour of Dirac particles in a class of Gödel-type space-time backgrounds in the presence of non-minimal coupling of the gravitational field with background curvature. We obtain the allowed energies for this relativistic system by solving analytically the Dirac equation in flat and curved space in a topologically trivial flat Gödel-type metric, and analyze the effects on the energy eiegnvalues.

Wave Fronts in a Causality-Violating Gödel-Type Metric

“…A particularly simple Type D metric has recently examined a member of a linear class of Gödel-type metrics [5]. Previously, relativistic quantum motion of spin-0 particle without interactions [6], linear confinement of a scalar particle subject to a scalar and vector potentials of Coulomb-types [7], Dirac equation [8], spin-0 system of DKP equation [9], and DKP oscillator [10] was investigated in this Type D metric.…”

“…In cylindrical coordinates ðt, r, ϕ, zÞ, the general class of Gödel-type metrics is given by [8,[11][12][13]]…”

Investigation of a Spin-0 Massive Charged Particle Subject to a Homogeneous Magnetic Field with Potentials in a Topologically Trivial Flat Class of Gödel-Type Space-Time

“…. Consider the following stationary space-time [50] (see [5,12,13,44,51]) in the Cartesian coordinates ðx 0 = t, x 1 = x, x 2 = y, x 3 = zÞ which is given by…”

“…where the spatial coordinates of the space-time are represented by x i and i, j = 1, 2, 3. The different classes of Gödeltype solutions have been discussed in [5]. Investigation of relativistic quantum dynamics of spinzero and spinhalf particles in the Gödel universe and Gödel-type space-times as well as the Schwarzschild and the Kerr black hole solution has been addressed by several authors.…”

“…The Fermi field with scalar and vector potentials in the Som-Raychaudhuri space-time was investigated in [32]. The Dirac particles in a flat class of Gödel-type space-time were studied in [5]. Dirac fermions in the ð1 + 2Þ-dimensional rotational symmetry space-time background were investigated in [33].…”