$\gamma$-Metrics in Higher Dimensions

TL;DR

This paper introduces new higher-dimensional gamma-metrics as exact vacuum solutions, analyzing their singularities, geodesic stability, redshift effects, and interior solutions in dimensions greater than five.

Contribution

It presents the first higher-dimensional gamma-metrics, explores their singularities, and provides interior solutions and physical property analyses for five-dimensional cases.

Findings

Higher-dimensional gamma-metrics are exact vacuum solutions.

Singularities depend on the deformation parameter gamma.

Stable circular orbits are characterized by effective potential analysis.

Abstract

We introduce five and higher dimensional $\gamma$-metrics. The higher dimensional metrics are exact solutions of the vacuum field equations and represent new types of singularities. For dimensions $d>5$ we have obtained $\gamma$-metrics in flat coordinates. We obtain singularities of metrics and for a better understanding of geometrical and physical properties of the five dimensional metric, stable circular orbits are determined by means of the effective potential. Effect of the deformed parameter ($\gamma$) on redshift of the $\gamma$-metric are calculated. Interior solution for the five-dimensional $\gamma$-metric is also obtained.