The influence of the Lande g -factor in the classical general relativistic description of atomic and subatomic systems

Abstract

Abstract. We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity via the introduction of an arbitrary Lande g-factor in the Kerr-Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the g-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.

Pseudo-Newtonian planar circular restricted 3-body problem

“…[23]). Hence, let us apply the outlined procedure to a concrete example, a source whose multipole structure is given by…”

“…From the previous, it can be inferred that once we know the gravitational multipole moments, and following the inverse procedure, it is possible to determinate approximate expressions for the gravitational potential ξ, in terms of the physical parameters of the source (see e.g. [23]). Hence, let us apply the outlined procedure to a concrete example, a source whose multipole structure is given by…”

Stealth chaos due to frame-dragging

“…The fact that the vorticity scalar can also be sourced through the electromagnetic field, naturally allows for a new scenario to study the suppression of chaos. However, the presence of an electric charge monopole also induces a prolate contribution to quadrupole deformation, which tends to generate chaotic dynamics [49]. The bottom panel of figure 4 shows how the electric charge of the source creates new chaotic zones, but as spin is increased from j = 0.0 to j = 0.06, these chaotic structure is not suppressed as efficiently as in the previous section.…”

“…To understand the behavior displayed in the examples shown in the previous two sections, let us consider the complex Ernst potential ξ, which has a direct relation to the Newtonian gravitational potential [35,49,50] and from which the multipole moments in equation (3) were derived [50]. By performing a Taylor expansion of ξ(ρ, z) in spherical coordinates (r, θ) at spatial infinity, its real R[ξ] and imaginary…”

Metric of a rotating charged magnetized sphere

“…It is easy to see that formulas (9) and (11) considerably simplify if the parameters j, e and µ are subject to the constraint µ = ej which represents the same gyromagnetic ratio of the electron as in the KN metric (see e.g. [18] for a discussion of this ratio in the context of exact electrovac solutions). In that subfamily, the potential E becomes an analytic function of Φ and hence such a 3-parameter subfamily can be treated within the framework of the well-known Ernst-Harrison (EH) charging transformation [6,19] involving the nonzero parameter e. Since in the known practical applications of the EH transformation the values of e are usually restricted to the "undercharged" case e < 1, it would be instructive to see how this transformation works in the "overcharged" case e > 1 too.…”