Some comments on a recently derived approximated solution of the Einstein equations for a spinning body with negligible mass

TL;DR

This paper critically evaluates a recently proposed approximate solution to Einstein's equations for a spinning body with negligible mass, analyzing its physical plausibility and potential experimental relevance.

Contribution

It derives geodesic equations for the solution and investigates the physical validity of the source tensor and the motions it permits.

Findings

Questions the physical realizability of the source tensor

Identifies potential unphysical features in the solution

Provides insights into the solution's applicability at Earth scales

Abstract

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks since the conditions of validity of the considered metric are well satisfied at Earth laboratory scales. However, it should be pointed out that reasonable doubts exist if it is physically meaningful because it is not clear if the source tensor related to the adopted metric can be realized by any real extended body. Here we derive the geodesic equations of the metric and analyze the allowed motions in order to disclose possible unphysical features which may help in shedding further light on the real nature of such approximated solution of the Einstein equations.