# On Properties of Expansion-free Dynamical Stars

## TL;DR

This paper investigates the unique geometrical and dynamical properties of expansion-free stars in general relativity, revealing conditions for their existence and conformal flatness when accelerating and radiating.

## Contribution

It provides new theoretical insights into the conditions under which expansion-free dynamical stars can exist and their geometric properties in general relativity.

## Key findings

- Stars must accelerate and radiate simultaneously for trapping to occur.
- If either acceleration or radiation is zero, the star is static with zero shear.
- Expansion-free dynamical stars are conformally flat when they accelerate and radiate.

## Abstract

We study the geometrical and dynamical features of expansion-free dynamical stars in general relativity. Such stars can exist only if particular physical and geometric conditions are satisfied. Firstly, for trapping to exist in an expansion-free dynamical star, the star must accelerate and radiate simultaneously. If either are zero, then the shear \(Sigma\) must be zero through out the star, in which case the star is static (\(\Theta=\Sigma=0\)). Secondly, we prove that with nonzero acceleration and radiation expansion-free dynamical stars must be conformally flat.