Slow Kerr-NUT black hole solution in dynamical Chern-Simons modified gravity

TL;DR

This paper investigates slow Kerr-NUT black hole solutions within dynamical Chern-Simons gravity, revealing how NUT and rotation parameters influence the metric and scalar field in a linear approximation.

Contribution

It provides a novel analysis of slow Kerr-NUT spacetime in dynamical Chern-Simons gravity, highlighting the effects of NUT and rotation parameters on the scalar field and metric.

Findings

Scalar field unaffected by NUT parameter without potential

Mixed metric component does not contribute at first order

Scalar field influenced by rotation and NUT parameters

Abstract

The slow rotation of Kerr-NUT spacetime is explored by taking into account the linear form of rotation and NUT parameters in the dynamical Chern-Simon gravity theory, which can be formulated from a scalar field describing the background. We show that in the absence of the potential scalar field, the metric potential does not respect the effect of the NUT parameter, although the scalar field is affected by the rotation and NUT parameters. Consequently, unlike the gradually spinning black hole solution outlined in \cite{Alexander:2009tp}, the mixed component of the metric potential, encompassing both rotational and NUT parameters, doesn't make a contribution at the primary level of the initial perturbation.