A family of well-behaved Karmarkar spacetime describing interior of relativistic stars

TL;DR

This paper introduces a new family of exact solutions for relativistic anisotropic stars using Class I embedding, ensuring physical viability and consistency with observed stellar properties, and analyzes their behavior for various neutron stars.

Contribution

It presents a novel family of well-behaved exact solutions for anisotropic stellar models based on five-dimensional embedding, applicable to different neutron stars with specific parameter ranges.

Findings

Solutions satisfy all energy conditions and Buchdahl limit.

Well-behaved solutions depend on the index n, with specific ranges for different stars.

Solutions exhibit physically acceptable properties within certain n ranges.

Abstract

We are presenting a family of new exact solutions for relativistic anisotropic stellar objects by considering four dimensional spacetime embedded in five dimensional Pseudo Euclidean space known as Class I solutions. These solutions are well-behaved in all respects, satisfy all energy conditions and the resulting compactness parameter is also within Buchdahl limit. The well-behaved nature of the solutions for a particular star solely depends on index n. We have discussed the solutions in detail for the neutron star XTE J1739-285 (M = 1.51M$\odot$, R = 10.9 km). For this particular star, the solution is well behaved in all respects for $8 \le n \le 20$. However, the solutions with n < 8 possess increasing trend of sound speed and the solutions belong to n > 20 disobey causality condition. Further, the well-behaved nature of the solutions for PSR J0348+0432 (2.01M$\odot$, 11 km), EXO 1785-248 (1.3M$\odot$, 8.85 km) and Her X-1 (0.85M$\odot$, 8.1 km) are specified by the index n with limits $24 \le n \le 54$, $1.5 \le n \le 4$ and $0.8 \le n \le 2.7$ respectively.