# Self-consistent description of a spherically-symmetric gravitational collapse

## TL;DR

This paper presents a self-consistent model of spherical gravitational collapse, showing that ideal fluids cannot form black holes and predicting a finite, regular firewall at the apparent horizon.

## Contribution

It derives a unique limiting form of the metric near the horizon, demonstrating the incompatibility of ideal fluid collapse with black hole formation and quantum energy conditions.

## Key findings

- Null energy condition is violated at the apparent horizon.
- Ideal fluid collapse cannot produce black holes.
- A finite, regular firewall forms at the expanding apparent horizon.

## Abstract

In spherical symmetry, the total energy-momentum tensor near the apparent horizon is identified up to a single function of time from two assumptions: a trapped region forms at a finite time of a distant observer, and values of two curvature scalars are finite at its boundary. In general relativity, this energy-momentum tensor leads to the unique limiting form of the metric. The null energy condition is violated across the apparent horizon and is satisfied in the vicinity of the inner apparent horizon. As a result, homogenous collapse models cannot describe the formation of a black hole. Properties of matter change discontinuously immediately after formation of a trapped region. Absolute values of comoving density, pressure, and flux coincide at the apparent horizon. Thus, collapse of ideal fluids cannot lead to the formation of black holes. Moreover, these three quantities diverge at the expanding apparent horizon, producing a regular (i.e., finite curvature) firewall. This firewall is incompatible with quantum energy inequalities, implying that trapped regions, once formed at some finite time of a distant observer, cannot grow.