Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes

TL;DR

This paper derives an exact formula for Lense-Thirring precession in Plebański-Demiański spacetimes, encompassing various axisymmetric solutions, and reveals the influence of NUT charge on precession even when the Kerr parameter is zero.

Contribution

It provides a unified exact expression for Lense-Thirring precession in Plebański-Demiański spacetimes, including extremal cases, and explores the effects of NUT charge on precession.

Findings

Exact Lense-Thirring precession rate derived for Plebański-Demiański spacetimes.

Precession does not vanish with zero Kerr parameter if NUT charge is present.

General extremal condition formulated for stationary axisymmetric spacetimes.

Abstract

An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first derive the general extremal condition for PD spacetimes. This general result could be applied to get the extremal limit in any stationary and axisymmetric spacetimes.