Formalism for Primordial Black Hole Formation in Spherical Symmetry

TL;DR

This paper develops a detailed formalism in spherical symmetry to predict primordial black hole formation and determine their masses, integrating various approaches and providing numerical implementation guidance.

Contribution

It introduces a comprehensive formalism based on Misner, Sharp, and Hernandez formalisms for primordial black hole formation, with rigorous derivations and connections to existing methods.

Findings

Formalism accurately predicts black hole formation.

Provides methods to extract black hole mass.

Includes implementation details and simulations.

Abstract

We present a comprehensive formalism for the description of primordial black hole formation in spherical symmetry based on the formalisms of Misner, Sharp, and Hernandez, which can be used to predict whether or not a black hole will form, and extract the resulting black hole mass when formation does occur. Rigorous derivations of all aspects of the formalism are provided, including a thorough investigation of appropriate initial and boundary conditions. We connect our formalism with numerous other approaches in the literature. Some implementation details for numerical code are provided. We include animations of simulated primordial black hole formation as supplemental material.