Event horizons and apparent horizons in spherically symmetric geometries

TL;DR

This paper demonstrates that in spherically symmetric electrovacuum spacetimes, apparent horizons coincide with event horizons, and describes their properties and propagation without relying on the Birkhoff theorem.

Contribution

It shows that apparent horizons and event horizons are equivalent in spherically symmetric electrovacuum spacetimes without using the Birkhoff theorem.

Findings

Apparent horizons have fixed area when outside a collapsing body.

Apparent horizons propagate outward at the speed of radially outgoing photons.

In electrovacuum, apparent horizons and event horizons are identical.

Abstract

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, have a fixed area and must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of the (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coincide with event horizons in electrovacuum.