Comments on Gravitoelectromagnetism of Ummarino and Gallerati in "Superconductor in a weak static gravitational field" vs Other Versions

TL;DR

This paper compares the gravitoelectromagnetic equations of Ummarino and Gallerati with previous models, showing their consistency with the correspondence principle and relevance to recent gravitational wave and gravitomagnetism experiments.

Contribution

It demonstrates that UG's gravitoelectromagnetic equations align with established Maxwellian Gravity in the non-relativistic limit and satisfy the correspondence principle, clarifying their theoretical standing.

Findings

UG equations match Maxwellian Gravity in the non-relativistic limit

UG equations satisfy the correspondence principle

Many other linearized GR equations do not satisfy the cp

Abstract

Recently reported [Eur. Phys. J. C., ${\bf 77}$, 549 (2017)] gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their linearized version of General Relativity (GR) are shown to match with (a) our previously reported special relativistic Maxwellian Gravity equations in the non-relativistic limit and with (b) the non-relativistic equations derived here, when the speed of gravity $c_g$ (an undetermined parameter of the theory here) is set equal to $c$ (the speed of light in vacuum). Seen in the light of our new results, the UG equations satisfy the Correspondence Principle (cp), while many other versions of linearized GR equations that are being (or may be) used to interpret the experimental data defy the cp. Such new findings assume significance and relevance in the contexts of recent detection of gravitational waves and the gravitomagnetic field of the spinning earth and their interpretations. Being well-founded and self-consistent, the equations may be of interest and useful to researchers exploring the phenomenology of gravitomagnetism, gravitational waves and the novel interplay of gravity with different states of matter in flat space-time like UG's interesting work on superconductors in weak gravitational fields.