Relativistic Charged Star Solutions in Higher Dimensions

Abstract

We present a class of relativistic solutions of the Einstein-Maxwell equations for a spherically symmetric charged static fluid sphere in higher dimensions. The interior space at t=constant considered here possess (D−1) dimensional spheroidal geometry described by a higher dimensional Vaidya-Tikekar metric. A class of new static solutions of coupled Einstein-Maxwell equations is obtained in a D-dimensional space-time by prescribing the geometry of a (D−1) dimensional hyper spheroid in hydrostatic equilibrium. The solutions of the Einstein-Maxwell field equations are employed to obtain relativistic models for charged compact stars with a suitable law for variation of electric field in terms of the charged fluid content in the interior of the sphere. The central density is found to depend on the space-time dimensions and a physically realistic model is permitted for (D≥4). The validity of both Strong Energy Condition (SEC), Weak Energy Condition (WEC) are studied for a given configuration and compactness of compact objects. We found new class of solutions with interesting stellar models where it permits a star with a core having different property than the rest which however disappears in higher dimensions. The effect of dimensions on the Electric charge of the compact object is studied. We note that the upper limit of the electric field is determined by the space-time dimensions which are determined.