# Phase transitions in neutron stars and their links to gravitational waves

## TL;DR

This paper reviews how gravitational wave observations, especially from events like GW170817, can reveal phase transitions in neutron star cores, potentially indicating quark matter presence through g-mode signals.

## Contribution

It provides a comprehensive review of neutron star matter, the equation of state, and how multimessenger observations constrain phase transitions within neutron stars.

## Key findings

- Detection of g-modes could signal hadron-quark phase transitions.
- Gravitational wave data constrains neutron star core composition.
- Observations suggest possible existence of quark matter in neutron stars.

## Abstract

The recent direct observation of gravitational wave event $GW170817$ and its $GRB170817A$ signal has opened up a new window to study neutron stars and heralds a new era of Astronomy referred to as the Multimessenger Astronomy. Both gravitational and electromagnetic waves from a single astrophysical source have been detected for the first time. This combined detection offers an unprecedented opportunity to place constraints on the neutron star matter equation of state. The existence of a possible hadron-quark phase transition in the central regions of neutron stars is associated with the appearance of g-modes, which are extremely important as they could signal the presence of a pure quark matter core in the centers of neutron stars. Observations of g-modes with frequencies between 1 kHz and 1.5 kHz could be interpreted as evidence of a sharp hadron-quark phase transition in the cores of neutron stars. In this article, we shall review the description of the dense matter composing neutron stars, the determination of the equation of state of such matter, and the constraints imposed by astrophysical observations of these fascinating compact objects.