Abstract
We have provided here a new class of interior solutions for anisotropic stars admitting conformal motion in higher dimensional noncommutative spacetime. The Einstein fields equations are solved by choosing a particular density distribution function of Lorentzian type \cite{Nozari} under noncommutative geometry. Several cases with dimensions $4D$ and higher, e.g. $5D$, $6D$ and $11D$ have been discussed separately. An overall observation is that the model parameters, such as density, radial pressure, transverse pressure, anisotropy all are well behaved and represent a compact star with radius $4.17$ km. However, emphasis has been given on the acceptability of the model from physical point of view. As a consequence it is observed that higher dimensions, i.e. beyond $4D$ spacetime, exhibit several interesting yet bizarre features which are not at all untenable for a compact stellar model of strange quark type and thus dictates a possibility of its extra dimensional existence.
Highlights
To model a compact object it is generally assumed that the underlying matter distribution is homogeneous, i.e. we have a perfect fluid, obeying the Tolman–Oppenheimer– Volkoff (TOV) equation
The vector uμ is the fluid (n + 2)-velocity and ημ is the unit spacelike vector which is orthogonal to uμ, where ρ is the matter density, pr is the radial pressure in the direction of ημ, and pt is the transverse pressure in the direction orthogonal to pr
In the present paper we have studied thoroughly a set of new interior solutions for anisotropic stars admitting conformal motion in higher-dimensional noncommutative spacetime
Summary
To model a compact object it is generally assumed that the underlying matter distribution is homogeneous, i.e. we have a perfect fluid, obeying the Tolman–Oppenheimer– Volkoff (TOV) equation. Contrary to this work Bhar [33] has studied a higher-dimensional charged gravastar admitting conformal motion, whereas a relativistic star admitting conformal motion has been analyzed by Rahaman et al [34] Inspired by this earlier work on conformal motion we are looking for a new class of solutions of anisotropic stars under the framework of general relativity inspired by noncommutative geometry in 4- and higherdimensional spacetimes. In the presence of noncommutative geometry there are two different distributions available in the literature: (a) Gaussian and (b) Lorentzian [2] Though these two mass distributions represent similar quantitative aspects, for the present investigation we are exploiting a particular Lorentzian-type energy density of the static spherically symmetric smeared and particle-like gravitational source in the multi-dimensional general form [1,2].
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