Horizons

TL;DR

This paper generalizes the definitions of black holes and horizons in Lorentzian geometry without assuming asymptotic flatness, exploring their properties and implications for cosmic censorship.

Contribution

It introduces new, conformally invariant definitions of horizons and black holes applicable to general manifolds, extending previous concepts beyond asymptotically flat spacetimes.

Findings

Different notions of horizons are conformally invariant.

Black hole notions are shown to be genuinely geometric.

Connections between various horizon definitions are established.

Abstract

We define different notions of black holes, event horizons and Killing horizons for a general time-oriented manifold $(M,g)$ extending previous notions but without the assumption of asymptotical flatness. The notions of 'horizon' are always conformally invariant while the notions of 'black hole' are genuinely geometric. Some connections between the different notions are found. Finally, we put the definitions into the context of the weak cosmic censorship conjecture.