A Precise Ultra - Dense Star Model on Spheroidal Space-Time

TL;DR

This paper develops an exact analytical model of a superdense relativistic star with a spheroidal interior, demonstrating its physical validity, stability, and relevance to neutron star properties using Einstein's equations.

Contribution

It introduces a new exact solution for a superdense star modeled as a spheroid, satisfying energy conditions and stability criteria, expanding the understanding of relativistic stellar configurations.

Findings

Model matches neutron star mass and radius ranges.

Solutions satisfy energy conditions and hydrostatic equilibrium.

Identifies stability condition at density ratio λ=0.4.

Abstract

This study presents a static, spherically symmetric configuration in which the interior geometry of a relativistic superdense star is modeled as a three-spheroid with constant $t_1$. The model is constructed using an analytical closed-form solution to Einstein's field equations. Assuming a characteristic density of $\rho_{a}= 2\times10^{14} \mathrm{g\,cm^{-3}}$, we compute the total mass and radius of the star based on a prescribed set of structural parameters that influence the density profile. The resulting stellar configurations exhibit boundary radii and total masses comparable to those of neutron stars with vanishing charge density. New exact solutions are obtained by solving the relevant second-order ordinary differential equations. We demonstrate that these solutions satisfy the standard energy conditions and maintain hydrostatic equilibrium throughout the stellar interior. All physical requirements remain valid at every point within the configuration. In this framework, the parameter $\lambda=\frac{\rho_{a}}{\rho_{0}}$ serves as a key determinant of the mass-radius relationship. We further assess the suitability of the model for representing a relativistic superdense star and analyze its stability under radial perturbations. The investigation indicates that, for the configuration to remain dynamically stable, the density ratio between the outer and inner regions must take the value $\lambda = 0.4$.