# Exact solutions for compact stars with CFL quark matter

## TL;DR

This paper derives exact solutions for compact stars composed of color-flavor locked (CFL) quark matter, linking microphysical properties to macroscopic stellar models within general relativity.

## Contribution

It introduces two families of exact solutions for anisotropic compact stars using a CFL quark matter equation of state, bridging microphysics and relativistic stellar modeling.

## Key findings

- Exact solutions for CFL quark stars obtained
- Models incorporate anisotropy and microphysical parameters
- Results connect microphysics with observable stellar properties

## Abstract

The search for the true ground state of the dense matter remains open since Bodmer, Terazawa and other raised the possibility of stable quarks, boosted by Witten's $strange$ $matter$ hypothesis in 1984. Within this proposal, the strange matter is assumed to be composed of $strange$ quarks in addition to the usual $up$s and $down$s, having an energy per baryon lower than the strangeless counterpart, and even lower than that of nuclear matter. In this sense, neutron stars should actually be strange stars. Later work showed that a paired, symmetric in flavor, color-flavor locked (CFL) state would be preferred to the one without any pairing for a wide range of the parameters (gap $\Delta$, strange quark mass $m_s$, and bag constant B). We use an approximate, yet very accurate, CFL equation of state (EoS) that generalizes the MIT bag model to obtain two families of exact solutions for the static Einstein field equations constructing families anisotropic compact relativistic objects. In this fashion, we provide exact useful solutions directly connected with microphysics.