Klein–Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies

Abstract

We argue that only exact, comprehensive, and explicit solutions for the fundamental models (i.e., the Klein-Gordon (KG) oscillators and the KG-Coulomb) would help to understand and describe the effects of gravitational fields on the dynamics of such quantum mechanical systems. In the current methodical proposal, the effects of the gravitational fields generated by a Gödel-type Som-Raychaudhuri (SR) cosmic string spacetime on KG-oscillators (KG-particles in general) are studied and reported. In so doing, we revisit the KG-oscillators in a topologically trivial Gödel-type spacetime background and use textbook procedures to report its exact solution that covers even and odd parities. Next, we discuss the drawbacks associated with the power series expansion approach that implies the biconfluent Heun functions/polynomials solution. We, therefore, recollect the so called pseudo perturbative shifted ` expansion technique (PSLET) as an alternative and more sophisticated method/technique. Illustrative examples are used: (i) a KG-oscillator in a topologically trivial Gödel-type spacetime, (ii) a quasi-free KG-oscillator in Gödel SR-type cosmic string spacetime, (iii) a KG-Coulombic particle in Gödel SR-type cosmic string spacetime at zero vorticity, and (iv) a massless KG-particle in Gödel SR-type cosmic string spacetime in a Cornell-type Lorentz scalar potential. The corresponding exact energies are obtained from the zeroth (leading) order correction of PSLET, where all higher order correction identically vanish. The comprehensive exactness of the reported solutions manifestly suggest degeneracies associated with spacetime (STAD) phenomenon.

PDM KG-Coulombic particles in cosmic string rainbow gravity spacetime and a uniform magnetic field

“…where D µ is the gauge-covariant derivative given by D µ = ∂ µ − ieA µ , and m is the rest mass energy of the KGparticle. At this point, we may also include position-dependent mass (PDM) settings (a metaphoric description of deformed coordinates and inherited from the von Roos Hamiltonian [37] ) using the PDM-momentum operator pj [38][39][40][45][46][47][48][49]. In this case,…”

“…Basically, for the PDM von Roos Schrödinger Hamiltonian [37], it has been shown (c.f., e.g., [38][39][40]) that the PDM momentum operator takes the form pj (r) = −i[∂ j − ∂ j f (r)/4f (r)] ; j = 1, 2, 3, where f (r) is a positive-valued dimensionless scalar multiplier. For more details on this issue the reader may refer to [38,40,[45][46][47][48][49]. This assumption would, in turn, allow one to cast the PDM von Roos kinetic energy operator (using = 2m = 1 units in the von Roos Hamiltonian) as T (r)ψ(r) = −f (r) −1/4 (∇ f (r) −1/2 ) • (∇ f (r) −1/4 ψ(r)) (known in the literature as Mustafa-Mazharimousavi's PDM kinetic energy operator [39]).…”

Dirac fermions in a spinning conical Gödel-type spacetime

“…On the other hand, in recent years an interesting proposal has emerged to work with Gödeltype solutions (or Gödel-type metrics) in the presence of a cosmic string, which has resulted in various papers on the subject, mainly in the area of RQM [82][83][84][85][86][87][88][89][90][91][92]. Explicitly, the general Gödel-type metric (actually the line element) in the presence of a (static) cosmic string in cylindrical coordinates (t, r, ϕ, z) with signature (+, −, −, −) is written as follows (c = G = 1) [82][83][84][85][86][87][88][89][90][91][92]…”

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

“…This parameter arose as a result of an exact equivalence between the Aharonov-Bohm effect and the Aharonov-Casher effect (both for spin-1/2 Dirac fermions) [99]. It is interesting to mention that recently the conical Gödel-type spacetime has been studied in the Klein-Gordon [100,101].…”