Superdense star in a space-time with minimal length

Abstract

In this paper we generalise core-envelope model of superdense star to a non-commutative space-time and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein's field equation in $\kappa$-deformed space-time and use this to set up non-commutative version of core-envelope model describing superdense stars. We derive $\kappa$-deformed law of density variation, valid up to first order approximation in deformation parameter and obtain radial and tangential pressures in $\kappa$-deformed space-time. We also derive $\kappa$-deformed strong energy conditions and obtain a bound on the deformation parameter.