A class of rotating metrics in the presence of a scalar field

TL;DR

This paper introduces a new class of rotating, axially symmetric metrics derived from static solutions with scalar fields, analyzing their properties, singularities, quasi-normal modes, and gyroscopic precession.

Contribution

It presents a novel rotating metric class that generalizes known solutions like JNW and gamma metrics, including their physical properties and observational signatures.

Findings

Rotating metrics are asymptotically flat, stationary, and axisymmetric.

Singularities of the rotating metrics are characterized.

Quasi-normal modes are computed in the eikonal limit.

Abstract

We consider a class of three parameter static and axially symmetric metrics that reduce to the Janis-Newman-Winicour (JNW) and $ \gamma$-metrics in certain limits of the parameters. We obtain rotating form of the metrics that are asymptotically flat, stationary and axisymmetric. In certain values of the parameters, the solutions represent the rotating JNW metric, rotating $ \gamma$-metric and Bogush-Gal'tsov (BG) metric. The singularities of rotating metrics are investigated. Using the light-ring method, we obtain the quasi normal modes (QNMs) related to rotating metrics in the eikonal limit. Finally, we investigate the precession frequency of a test gyroscope in the presence of the rotating metrics.