# Effects of Hadron-Quark Phase Transitions in Hybrid Stars within the NJL Model

## TL;DR

This paper investigates phase transitions in hybrid stars using NJL models, analyzing their impact on observable signatures and oscillation modes, and compares different phase transition formalisms against astrophysical data.

## Contribution

It introduces a detailed comparison of local and non-local NJL models for quark matter in hybrid stars, including observational signatures and oscillation mode analysis.

## Key findings

- Hybrid star models with phase transitions match observational data.
- Mixed phase signatures differ from sharp first-order transitions.
- Discontinuities in the equation of state affect g-mode oscillations.

## Abstract

We study local and non-local Polyakov Nambu-Jona-Lasinio models and analyze their respective phase transition diagram. We construct hybrid stars using the zero temperature limit of the local and non-local versions of Nambu-Jona-Lasinio model for quark matter and the modern GM1(L) parametrization of the non-linear relativistic mean field model for hadronic matter. We compare our models with data from PSR J1614-2230 and PSR J0343+0432 and also from GW170817 and its electromagnetic counterpart GRB170817A and AT2017gfo. We study observational signatures of the appearance of a mixed phase as a result of modeling a phase transition that mimics the Gibbs formalism and compare the results with the sharp first-order phase transition obtained using the Maxwell construction. We also study in detail the $g$-mode associated with discontinuities in the equation of state, and calculate non-radial oscillation modes using relativistic Cowling approximation.