# Superdense star in a space-time with minimal length

## TL;DR

This paper extends the core-envelope model of superdense stars to non-commutative space-time, incorporating quantum gravity effects via a minimal length and deriving modified Einstein equations and physical conditions.

## Contribution

It introduces a $$-deformed model of superdense stars, deriving new density, pressure, and energy condition relations in non-commutative space-time.

## Key findings

- Derived $$-deformed Einstein equations.
- Established bounds on the deformation parameter.
- Obtained modified density and pressure profiles.

## 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.