A class of Taub-NUT-scalar metrics via Ehlers transformations

TL;DR

This paper constructs new Taub-NUT scalar metrics using Ehlers transformations, analyzes their physical properties including geodesics and lensing, and generates additional solutions via conformal transformations, advancing understanding of scalar-tensor gravity solutions.

Contribution

It introduces a novel class of Taub-NUT scalar metrics derived through Ehlers transformations and explores their physical and geometric properties.

Findings

Derived new Taub-NUT-scalar metrics using Ehlers transformations.

Analyzed geodesics, topological charge, and light deflection in these metrics.

Generated new solutions in Einstein-conformal-scalar theory via conformal transformations.

Abstract

We derive a class of Taub-NUT metrics in the presence of a scalar field (TNS) by using Ernst equations and potential, as well as using Ehlers transformations on the exact solutions that was recently introduced in Azizallahi et al. (Nucl Phys B 998:116414, https://doi.org/10.1016/j.nuclphysb.2023.116414, arXiv:2307.09328 [gr-qc], 2023) and Mirza et al. (Eur Phys J C 83:1161, https://doi.org/10.1140/epjc/s10052-023-12255-7, arXiv:2307.13588 [gr-qc], 2023). Furthermore, we investigate the effective potential, geodesics, topological charge, quasinormal modes (QNMs) and the deflection angle of light in a gravitational lensing for the obtained class of TNS metrics. We also use conformal transformations to generate a new class of exact solutions of the Einstein-conformal-scalar theory by using the obtained TNS solutions as seed metrics. Finally we compare QNMs of the class of exact solutions.