Three parameter metrics in the presence of a scalar field in four and higher dimensions

TL;DR

This paper explores a family of three-parameter metrics influenced by scalar fields, analyzing their properties in four and higher dimensions, including curvature, potential, and frequencies, extending known metrics like the gamma and JNW metrics.

Contribution

It introduces a generalized class of metrics with scalar fields in multiple dimensions, analyzing their geometric and physical properties and extending existing models.

Findings

Derived properties of the metrics, including curvature invariants and effective potential.

Extended the metrics to five and higher dimensions with scalar fields.

Connected the new metrics to known solutions like the gamma and JNW metrics.

Abstract

We investigate a class of three parameter metrics that contain both the $\gamma$-metric and Janis-Newman-Winicour (JNW) metric at special values of the parameters. To see the effect of the scalar field we derive some properties of this class of metrics such as curvature invariants, the effective potential, and epicyclic frequencies. We also introduce the five and higher dimensional forms of the class of metrics in the presence of a scalar field.