Space time and rotations

TL;DR

This paper derives the metric of spacetime around a rotating, weakly gravitating body, providing both external and internal solutions, with effects potentially observable in laboratory experiments.

Contribution

It presents a consistent calculation of the space-time metric and source tensor for a rotating body in the weak-field approximation, focusing on rotation effects over mass effects.

Findings

Non-zero Riemann tensor indicating spacetime curvature.

Predicted effects are measurable at laboratory scale.

External and internal metrics are explicitly derived.

Abstract

The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are calculated at the lowest meaningful approximation in a power series. The two physical parameters entering the equations (the mass and the angular momentum per unit mass) are assumed to be such that the mass effects are negligible with respect to the rotation effects. A non zero Riemann tensor is obtained. The order of magnitude of the effects at the laboratory scale is such as to allow for experimental verification of the theory.