Superconductor in a weak static gravitational field

Abstract

We provide the detailed calculation of a general form for Maxwell and London equations that takes into account gravitational corrections in linear approximation. We determine the possible alteration of a static gravitational field in a superconductor making use of the time-dependent Ginzburg-Landau equations, providing also an analytic solution in the weak field condition. Finally, we compare the behavior of a high-T c superconductor with a classical low-T c superconductor, analyzing the values of the parameters that can enhance the reduction of the gravitational field.

Comments on gravitoelectromagnetism of Ummarino and Gallerati in “Superconductor in a weak static gravitational field” vs other versions

“…3). From McDonald's [4] report of little known Heaviside's Gravity (HG) [4,5] of 1893, 3 we find that the equations of NRMG also match with those of HG in which Heaviside thought c g might be equal to c. These findings assume significance and relevance in the contexts of recent experimental detection of gravitational waves [6][7][8][9], gravito-magnetic field of the spinning Earth using the orbital data of two laser-ranged satellites (LAGEOS and LAGEOS II) [10][11][12][13][14] and the Gavity Probe B (GP-B) experimental results [15][16][17] vindicating Einstein's GR, because all of these results are being interpreted in the 1 Schwinger et al [2] derived (b) using the Galileo-Newton principle of relativity (masses at rest and masses with a common velocity viewed by a co-moving observer are physically indistinguishable). Here, we will use this relativity principle for deriving the gravitational analogue of the Lorentz force law.…”

“…In a recent interesting theoretical study on the interplay of superconductivity and weak static gravitational field, Ummarino and Gallerati [1] concluded that the reduction of the gravitational field in a superconductor, if it exists, is a transient phenomenon and depends strongly on the parameters that characterize the superconductor. The gravitational equations used by the authors in their study are represented by the following Gravito-Maxwell Equations: a e-mail: behera.hh@gmail.com…”

“…In the above equations ρ g = ρ 0 is the (rest) mass density, j g = ρ g v mass current density, the speed of gravitational waves in vacuum c g = c (the speed of light in vacuum) in [1], E g is the usual Newtonian gravitational field (called gravitoelectric field) and B g is the gravitational analogue of magnetic induction field (called gravito-magnetic field). The E g and B g fields are related to gravitoelectric scalar potential φ g and gravitomagnetic vector potential A g as…”

“…Ummarino and Gallerati [1] derived these equations from Einstein's GR by linearization procedure in the weak field and slow motion approximations. We name the Eqs.…”

“…We name the Eqs. (1)(2)(3)(4)(5)(6)(7) to represent the General Relativistic Maxwellian Gravity of Ummarino-Gallerati as (GRMG-UG) to differentiate it from other existing (or future) formulations that (may) result from different methods of study. For instance, in this communication we show how one can derive these equations in a nonrelativistic approach without invoking the space-time curvature and the linearization schemes of GR.…”