Exact solutions in (2 + 1)-dimensional anti-de Sitter space-time admitting a linear or non-linear equation of state

TL;DR

This paper derives exact solutions for (2+1)-dimensional anisotropic stars in anti-de Sitter space-time with linear or non-linear equations of state, matching interior models to the BTZ black hole exterior.

Contribution

It introduces two new classes of solutions for anisotropic stars in (2+1) dimensions with specific equations of state, expanding the understanding of lower-dimensional gravitational models.

Findings

Solutions are regular and well-behaved at the stellar interior.

Matching conditions with BTZ exterior are satisfied.

Models accommodate both linear and non-linear equations of state.

Abstract

Gravitational analyzes in lower dimensions has become a field of active research interest ever since Banados, Teitelboim and Zanelli (BTZ) (Phys. Rev. Lett. 69, 1849, 1992) proved the existence of a black hole solution in (2 + 1) dimensions. The BTZ metric has inspired many investigators to develop and analyze circularly symmetric stellar models which can be matched to the exterior BTZ metric. We have obtained two new classes of solutions for a (2 + 1)-dimensional anisotropic star in anti-de Sitter background space-time which have been obtained by assuming that the equation of state (EOS) describing the material composition of the star could either be linear or non-linear in nature. By matching the interior solution to the BTZ exterior metric with zero spin, we have demonstrated that the solutions provided here are regular and well-behaved at the stellar interior.