New class of relativistic anisotropic strange star in Vaidya-Tikekar model

Abstract

A new class of compact cold star with strange matter is obtained in a spheroidal space-time with anisotropic pressure described by Vaidya-Tikekar metric. Considering strange matter equation of state namely $p=\frac{1}{3}(\rho -4B)$, where $B$ is Bag constant in MIT Bag model, we determine the Mass-Radius relationship for Strange Star in four and higher dimensions using the value of surface density $\rho _{s}=4B$ with the allowed value of $B$ ($145~\text{MeV} < B^{\frac{1}{4}} <164.4~\text{MeV}$ or equivalently $57.55~\text{MeV}/\text{fm}^{3} < B < 95.11~\text{MeV}/\text{fm}^{3}$) with respect to neutron for stable strange matter with zero pressure condition. We found that for a constant $B$, a limiting value of the radius ($b$) of the star for which geometrical parameter $R$ is real within the allowed range of $B$ as mentioned above. We further note that in four dimension the compactness (ratio of mass to radius) of the star corresponding to the maximum radius is greater than 0.33 in isotropic case and increases when anisotropy increases. In case of five dimensions, we note that same type of nature with different values of compactness is observed. Causality condition holds good through out the star in this model up to a certain values of radius $b$ for which $R$ is real. The information about Mass-to-Radius ratio leads to the determination of total mass, radius and other physical parameters of the stellar configuration.