Local anisotropy of space in a frame of reference co-moving with the Earth

TL;DR

This paper investigates the local anisotropy of space around Earth within General Relativity, considering Earth's mass, shape, and rotation, and finds it to be detectable at very small scales.

Contribution

It provides a detailed analysis of space anisotropy in Earth's frame considering realistic Earth parameters, highlighting potential observability.

Findings

Local space anisotropy is of order 10^{-12} to 10^{-13}.

Anisotropy could be observed with current or near-future technology.

The analysis incorporates Earth's quadrupole moment and rotation effects.

Abstract

We consider, in the framework of General Relativity, the linear approximation of the gravitational field of the Earth taking into account its mass, its quadrupole moment, its shape and its diurnal rotation. We conclude that in the frame of reference co-moving with the Earth the local anisotropy of the space is of the order of $10^{-12}-10^{-13}$ and could be observed.