Multipolar corrections for Lense-Thirring precession

TL;DR

This paper derives a simple formula for Lense-Thirring precession using Ernst potentials, enabling calculation of non-spherical effects on gyroscope precession around Earth, with new estimations of these contributions.

Contribution

It introduces a straightforward expression for Lense-Thirring precession in stationary axially symmetric spacetimes, enhancing understanding of non-spherical effects.

Findings

Reproduces known results for non-spherical contributions

Provides new estimations for Earth's non-spherical precession effects

Uses weak field approximation for practical calculations

Abstract

For stationary axially symmetric spacetimes we find a simple expression for the Lense-Thirring precession in terms of the Ernst potential. This expression is used to compute, in the weak field approximation, the major non-spherical contributions to the precession of a gyroscope orbiting the Earth. We reproduce previously known results and give a new estimation for non-spherical contributions.