Possible Alterations of Local Gravitational Field Inside a Superconductor

Abstract

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.

Superconductors and Gravity

“…From a physical point of view, this choice also reflects the absence of localized charges inside the superfluid, while contributions to the total gravitational field originating from the sample mass are clearly totally irrelevant. The dimensionless TDGL then explicitly read [128]:…”

Interaction Between Macroscopic Quantum Systems and Gravity

“…Inspired by the experimental effects of gravitational fields on superfluids and supercurrents, Ummarino and Gallerati considered the possible back-reaction of the latter on the surrounding local gravitational field in some specific, favourable situations [90,91,93,94,147]. In particular, they analysed how the local gravitational field can be affected by the presence of a supercondensate, exploiting the time-dependent Ginzburg-Landau equations [148] in the regime of fluctuations [91] and in a more general situation [93,94]. Physical situations which cannot be consistently described in terms of the quasiparticle method or the mean field approximation are called fluctuations [149].…”

“…In [90,93] Ummarino and Gallerati consider the possible alteration of the local static gravitational field in the region inside the superconductor. To this end, they exploit the timedependent Ginzburg-Landau equations for the supercondensate order parameter, looking for analytic solutions in the weak field condition in the simple case of isolated isotropic superconductor, immersed in the Earth's gravity.…”

From Kerr to Heisenberg

“…coinciding in practice with (8). All this is in terms of global coordinates; if we wish to know what is locally measured by observer O we have to multiply by √ g 00 and we obtain…”

“…It is always true that we may locally diagonalize the metric (this happens because, apart from singularities, there always is a local tangent flat space-time); the diagonalization is however not contextually possible everywhere. The nickname "gravitomagnetism" (GM) is, as known, due to the fact that, in weak field approximation, the Einstein equations in vacuo assume a form practically coinciding (but for a factor of 2) with the classical Maxwell equations of electromagnetism (EM) and g 0i may, in the same approximation, be treated as the components of a three-dimensional vector potential in analogy with EM [3][4][5][6][7][8][9][10][11].…”