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

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.