Type II critical phenomena of neutron star collapse

TL;DR

This paper explores the critical collapse of neutron stars under general relativity, revealing that for a specific adiabatic index, the critical behavior matches that of ultrarelativistic fluids, with implications for black hole formation.

Contribution

It demonstrates that neutron star collapse exhibits Type II critical phenomena with a scaling exponent similar to ultrarelativistic fluids at a specific adiabatic index, extending understanding of critical collapse.

Findings

Critical solutions have similar scaling exponents for Gamma=2.

Neutron star collapse asymptotes to ultrarelativistic critical solutions.

Black holes of arbitrarily small mass can form at criticality.

Abstract

We investigate spherically-symmetric, general relativistic systems of collapsing perfect fluid distributions. We consider neutron star models that are driven to collapse by the addition of an initially "in-going" velocity profile to the nominally static star solution. The neutron star models we use are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic, gamma-law equation of state. The initial values of 1) the amplitude of the velocity profile, and 2) the central density of the star, span a parameter space, and we focus only on that region that gives rise to Type II critical behavior, wherein black holes of arbitrarily small mass can be formed. In contrast to previously published work, we find that--for a specific value of the adiabatic index (Gamma = 2)--the observed Type II critical solution has approximately the same scaling exponent as that calculated for an ultrarelativistic fluid of the same index. Further, we find that the critical solution computed using the ideal-gas equations of state asymptotes to the ultrarelativistic critical solution.