Initial data and black holes for matter models

TL;DR

This paper discusses the construction of initial data leading to black hole formation in matter models within general relativity, extending results to unbounded domains and analyzing the implications of different equations of state.

Contribution

It introduces methods for constructing initial data that result in black hole formation and extends existing results to unbounded domains for Einstein-perfect fluid systems.

Findings

Construction of admissible initial data for matter models

Extension of results to unbounded domains in spherical symmetry

Discussion of polytropic equations of state and regularity issues

Abstract

To observe the dynamic formation of black holes in general relativity, one essentially needs to prove that closed trapped surfaces form during evolution from initial data that do not already contain trapped surfaces. We discuss the recent development of the construction of such admissible initial data for matter models. In addition, we extend known results for the Einstein equations coupled to perfect fluids in spherical symmetry and with linear equation of state to unbounded domains. Polytropic equations of state and regularity issues with the direct application of the singularity theorems in general relativity are discussed briefly.