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$γ$-Metrics in Higher Dimensions

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 $γ$-metric are calculated. Interior solution for the five-dimensional $γ$-metric is also obtained.