New criterion for direct black hole formation in rapidly rotating stellar collapse

TL;DR

This study investigates the collapse of rapidly rotating relativistic stars, revealing that black holes can form even when the total spin exceeds unity, provided the central region’s spin parameter is below one, challenging previous beliefs.

Contribution

The paper introduces a new criterion based on the central spin parameter for black hole formation in rotating stellar collapse, supported by full general relativistic simulations.

Findings

Black holes can form from stars with total spin parameter q > 1.

The central spin parameter q_c determines black hole formation, with q_c < 1 being critical.

Simulations confirm predictions based on initial density and angular momentum profiles.

Abstract

We study gravitational collapse of rapidly rotating relativistic polytropes of the adiabatic index $\Gamma = 1.5$ and 2, in which the spin parameter $q \equiv J/M^{2} > 1$ where $J$ and $M$ are total angular momentum and gravitational mass, in full general relativity. First, analyzing initial distributions of the mass and the spin parameter inside stars, we predict the final outcome after the collapse. Then, we perform fully general relativistic simulations on assumption of axial and equatorial symmetries and confirm our predictions. As a result of simulations, we find that in contrast with the previous belief, even for stars with $q > 1$, the collapse proceeds to form a seed black hole at central region, and the seed black hole subsequently grows as the ambient fluids accrete onto it. We also find that growth of angular momentum and mass of the seed black hole can be approximately determined from the initial profiles of the density and the specific angular momentum. We define an effective spin parameter at the central region of the stars, $q_{c}$, and propose a new criterion for black hole formation as $q_{c} \alt 1$. Plausible reasons for the discrepancy between our and previous results are clarified.