Spin 0 and Spin 1/2 Particles in a Spherically Symmetric Static Gravity and a Coulomb Field

Abstract

A relativistic particle in an attractive Coulomb field as well as a static and spherically symmetric gravitational field is studied. The gravitational field is treated perturbatively and the energy levels are obtained for both spin 0 (Klein-Gordon) and spin 1/2 (Dirac) particles. The results are shown to coincide with each other as well as the result of the nonrelativistic (Schrödinger) equation in the nonrelativistic limit.

Black hole interference patterns in flavor oscillations

“…Unlike in the previous section, where the description was done in the equatorial plane θ = π/2, we follow convention for these studies and consider here a cylindrically symmetric system where the wave vector of the original plane wave is along the z-axis. In coordinates (16), the fields therefore depends on r and θ, but not ϕ.…”

“…General studies of gravitational effects on the phase of wave functions, for different spins, were done in [13], [14], [15], [16], [17], and more specific studies involve supernovae explosions [18], neutrino optics and the Lens-Thirring effect [19], or the study of three flavour oscillations in curved space time [20]. There is also a potential violation of the Equivalence Principle in relation to flavour oscillations in curved space time, as discussed in [21], [22], [23].…”

One-electron atoms in Schwarzschild universe: bare and electromagnetically dressed cases

“…Among others, two leading approaches are those by DeWitt [1] and Weber [2]. In the studies based on DeWitt's approach, the general formulation of quantum mechanics for a relativistic or non-relativistic system on a curved background is the main concern [3][4][5][6]. In the second based on Weber's, an interaction scheme between the quantum system and the gravitational field is the guiding rule.…”

“…Based on the DeWitt's approach, the formulation of Dirac particles on a curved background is used to extract the first corrections in curvature to the energy levels of one-electron atoms [3][4][5][6]. In [7,8], the interaction between gravitational waves and a charged test particle is studied.…”