Relativistic anisotropic star and its maximum mass in higher dimensions

We present a class of relativistic solutions of cold compact anisotropic stars in hydrostatic equilibrium in the framework of higher dimensions using spheroidal geometry. The solutions obtained with Vaidya-Tikekar metric are used to construct stellar models of compact objects and studied their physical features. The effects of anisotropy and extra dimensions on the global properties namely, compactness, mass, radius, equation of state are determined in higher dimensions in terms of the spheroidicity parameter ($λ$). It is noted that for a given configuration, compactness of a star is found smaller in higher dimensions compared to that in four space-time dimensions. It is also noted that the maximum mass of compact objects increase with the increase of space-time dimensions which however attains a maximum when $D=5$ for a large ($λ=100$), thereafter it decreases as one increases number of extra dimensions. The effect of extra dimensions on anisotropy is also studied.

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