Compact star in pseudo-spheroidal 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.