A class of interior solutions corresponding to a $(2+1)$ dimensional asymptotically anti-de Sitter spacetime

TL;DR

This paper derives a new class of interior solutions for isotropic stars in (2+1)-dimensional asymptotically anti-de Sitter spacetime, providing insights into lower-dimensional gravity and black hole physics.

Contribution

It introduces a novel analytical class of interior solutions matching the BTZ black hole exterior in (2+1) dimensions, with regularity and physical parameter analysis.

Findings

Solutions satisfy all regularity conditions

Analytical form simplifies physical parameter study

Provides insights into lower-dimensional gravity and black holes

Abstract

Lower dimensional gravity has the potential of providing non-trivial and valuable insight into some of the conceptual issues arising in four dimensional relativistic gravitational analysis. The asymptotically anti-de Sitter (2+1) dimensional spacetime described by Ba$\tilde{n}$ados, Teitelboim and Zanelli (BTZ) which admits a black hole solution, has become a source of fascination for theoretical physicists in recent years. By suitably choosing the form of the mass function $m(r)$, we derive a new class of solutions for the interior of an isotropic star corresponding to the exterior (2+1) asymptotically anti-de Sitter BTZ spacetime. The solution obtained satisfies all the regularity conditions and its simple analytical form helps us to study the physical parameters of the configuration in a simple manner.