# A General-relativistic Determination of the Threshold Mass to Prompt Collapse in Binary Neutron Star Mergers

## TL;DR

This paper develops a universal relation between the threshold mass for prompt collapse in binary neutron star mergers and the maximum compactness, improving previous models and using GW170817 data to constrain neutron star radii.

## Contribution

It introduces a novel, rigorous method to determine the threshold mass and establishes a nonlinear universal relation with maximum compactness, enhancing the accuracy over previous linear models.

## Key findings

- Existence of a nonlinear universal relation between threshold mass and maximum compactness.
- Improved accuracy of the threshold mass determination compared to previous linear models.
- Set lower limits on neutron star radii using GW170817 data and the new universal relation.

## Abstract

We study the lifetimes of the remnant produced by the merger of two neutron stars and revisit the determination of the threshold mass to prompt collapse, $M_{\rm th}$. Using a fully general-relativistic numerical approach and a novel method for a rigorous determination of $M_{\rm th}$, we show that a nonlinear universal relation exists between the threshold mass and the maximum compactness. For the temperature-dependent equations of state considered here, our results improve a similar linear relation found recently with methods that are less accurate but yield quantitatively similar results. Furthermore, exploiting the information from GW170817, we use the universal relation to set lower limits on the stellar radii for any mass.