Compact star in pseudo-spheroidal spacetime

TL;DR

This paper explores static, circularly symmetric perfect fluid stars in (2+1) dimensions within pseudo-spheroidal spacetime, providing new interior solutions compatible with the BTZ exterior metric and analyzing their physical properties.

Contribution

It introduces a class of interior solutions for (2+1)-dimensional stars with pseudo-spheroidal geometry linked to the BTZ black hole exterior, highlighting the role of spheroidicity parameter.

Findings

Existence of physically reasonable star solutions in (2+1) dimensions with BTZ exterior

The spheroidicity parameter influences star properties significantly

Solutions are consistent with asymptotically anti-de Sitter spacetime

Abstract

We investigate perfect fluid stars in $(2+1)$ dimension in pseudo spheroidal spacetime with the help of Vaidya-Tikekar metric where the physical $3$-space ($t=$ constant) is described by pseudo-spheroidal geometry. Here the spheroidicity parameter $a$, plays an important role for determining the properties of a compact star. In the present work a class of interior solutions corresponding to the Ba$\tilde{n}$ados-Teitelboim-Zanelli $(BTZ)$ (Ba\~nados et al., Phys. Rev. Lett. 69:1849, 1992) exterior metric has been provided which describes a static circularly symmetric star with negative cosmological constant in equilibrium. It is shown that asymptotically anti-de Sitter $(2+1)$ dimensional spacetime described by BTZ admits a compact star solution with reasonable physical features.