# Exploring density dependent B as a suitable parameter in higher dimensional approach with a non-linear equation of state

## TL;DR

This paper develops a higher-dimensional, singularity-free model of anisotropic compact stars using a non-linear equation of state, validated against observational data and demonstrating stability and wide applicability.

## Contribution

It introduces a density-dependent MIT bag model within a higher-dimensional framework, extending previous models and fitting observational data of pulsars.

## Key findings

- Model fits observational data of PSR J1614-2230
- Develops a polynomial equation of state of order five
- Demonstrates stability via multiple criteria

## Abstract

In this investigation, we present a singularity free interior solution of the Einstein field equation for a class of anisotropic compact objects in dimensions $D\geq4$. In accordance with the concept of Vaidya and Tikekar, the geometry of the physical $(D-1)$-space of a star corresponding to $t=constant$ hypersurface is assumed to be of a $(D-1)$ spheroid. For the fulfilment of causality condition, a limit of the spheroidal parameter ($\lambda$) is noted depending on the values of amount of anisotropy ($\alpha$) and space-time dimensions ($D$). We note that by switching off the extra parameters ($\alpha$ and $D$), previously obtained limit of $\lambda$ can be generated. To validate our findings, we compare the results obtained from our model with observational data of PSR J1614-2230 (mass=$1.908^{+0.016}_{-0.016}M_{\odot}$, radius=$11.93^{+0.50}_{-0.50}km$). It is noted that the best fit equation of state corresponds to polynomial equation of state of the order of five. We use this finding to develop a density dependent MIT bag model which seems to be useful for the correct description of compact object in our model. The mass radius relation shows that our model mimics a wide range of recently observed pulsars in four and higher dimensions. Furthermore, we also found that our model exhibits stability according to Generalised TOV equation, Herrera cracking condition, and the adiabatic index.