Central density cusps in the Lema\^{i}tre-Tolman solutions

TL;DR

This paper investigates the central density profiles of Lemaître-Tolman solutions, establishing conditions for black hole formation and exploring their role in cosmological modeling without a cosmological constant.

Contribution

It introduces a necessary condition for black hole development in LT solutions and analyzes the implications of central density cusps in cosmological and collapse scenarios.

Findings

Central density cusps are compatible with black hole formation.

A necessary condition for black hole development in LT solutions is derived.

LT solutions can model cosmological observations without a cosmological constant.

Abstract

The character of the central density profile in the Lema\^{i}tre-Tolman (LT) solutions plays a fundamental role in their application as cosmological models. This same character is studied here for these solutions used to model complete gravitational collapse. A necessary condition for the development of a black hole (not even locally naked singularities) is developed. This condition allows central density cusps, the central feature of the LT solutions when used to match cosmological observations without invoking the cosmological constant.