Connection between Lense–Thirring precession, Ernst potential and Thorne multipoles

Abstract

For stationary axially symmetric spacetimes we find a simple expression for the Lense–Thirring precession in terms of two scalar quantities, the real and imaginary parts of the Ernst potential. Its weak-field approximation is expressed in terms of Thorne multipoles and used to compute the major non-spherical contributions to the precession of a gyroscope orbiting around the Earth. We reproduce previously known results and give a new estimation for non-spherical contributions. We believe the present work has important applications in the interpretation of approximate as well as exact solutions of Einstein field equations.