Historical research guide · 0038 · 1991
Effects of a gravitomagnetic field on pure superconductors
Ning Li · D. Torr
In one minute
A pure superconductor expels ordinary magnetic field from its interior: the Meissner effect. In this 1991 paper, Ning Li and Douglas Torr ask how a pure superconductor behaves when external magnetic and gravitomagnetic fields are present together. Gravitomagnetism names the rotational part of the weak-field general-relativistic equations: the same formal structure that makes a moving charge magnetic couples a rotating mass to a gravitomagnetic field. Li and Torr combine the Maxwell, weak-field gravitational and London descriptions. Their stated result gives the internal fields in terms of the material's magnetic and gravitomagnetic permeabilities. They report a small residual uniform magnetic field, additional mutually induced internal perturbations, and a combined field that falls exponentially with distance inside the material. This sheet follows the paper's equations and stated results.
Connection
The paper gives chapter 11 a precise theoretical starting point: an equation-level coupling between the two field descriptions in a superconducting material. The question it opens is concrete: measure the internal fields, their characteristic length scales and their dependence on the material parameters.
From the source
Li and Torr solve the coupled Maxwell, general-relativistic and London equations for the internal magnetic and gravitomagnetic fields of a pure superconductor exposed to external gravitomagnetic and magnetic fields.Abstract; theory sections
The internal fields are given by expressions involving the gravitomagnetic and magnetic permeabilities of the superconductor, so the material's own properties set how strongly it responds.Abstract; results
Although the Meissner effect ordinarily excludes all magnetic field from the interior of a superconductor, the analysis finds that a small residual uniform magnetic field will pervade the superconductor.Abstract
The external gravitomagnetic and magnetic fields mutually induce additional small internal perturbation fields, and the two internal fields are related to one another through the Cooper-pair mass-to-charge ratio.Abstract; results
The combined field expression decays exponentially over a characteristic distance, consistent with the requirement that the sum vanishes deep inside the superconductor; the gravitomagnetic penetration depth is larger than the ordinary magnetic penetration depth.Abstract; discussion
The response expression makes a laboratory measurement specific: measure the material's magnetic and gravitomagnetic permeabilities, the induced internal fields and their characteristic penetration depths.Abstract; results
The way in
https://doi.org/10.1103/PhysRevD.43.457How to cite it
Ning Li, D. Torr (1991) Effects of a gravitomagnetic field on pure superconductors doi:10.1103/PhysRevD.43.457