How current loops and solenoids curve space-time

TL;DR

This paper models the space-time curvature caused by current loops and solenoids using Einstein-Maxwell equations, revealing gravitational effects and proposing an experiment to detect these effects with existing superconducting technology.

Contribution

It provides a numerical solution for the gravitational field of electromagnetic sources and suggests a feasible experiment to observe these effects.

Findings

Gravitational redshift caused by magnetic fields

Deviation of light in curved space-time around current-carrying coils

Proposed experimental setup with measurable phase shifts

Abstract

The curved space-time around current loops and solenoids carrying arbitrarily large steady electric currents is obtained from the numerical resolution of the coupled Einstein-Maxwell equations in cylindrical symmetry. The artificial gravitational field associated to the generation of a magnetic field produces gravitational redshift of photons and deviation of light. Null geodesics in the curved space-time of current loops and solenoids are also presented. We finally propose an experimental setup, achievable with current technology of superconducting coils, that produces a phase shift of light of the same order of magnitude than astrophysical signals in ground-based gravitational wave observatories.