γ-Metrics in higher dimensions

Abstract

We introduce five and higher dimensional γ-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 γ-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 (γ) on redshift of the γ-metrics are calculated. Interior solution for the five-dimensional γ-metric is also obtained.