On the existence of cosmological event horizon

TL;DR

This paper establishes conditions under which cosmological event horizons exist in static or axisymmetric spacetimes, linking their existence to violations of the strong energy condition, such as with a positive cosmological constant.

Contribution

It provides a general criterion for the existence of cosmological Killing horizons based on energy conditions in static and axisymmetric spacetimes.

Findings

A cosmological Killing horizon exists only if the Ricci tensor contracted with a hypersurface orthogonal vector is negative.

The existence of such horizons implies matter fields violate the strong energy condition.

Positive cosmological constant is a simple example of this violation.

Abstract

We show that, for general static or axisymmetric stationary spacetimes, a cosmological Killing horizon exists only if $R_{ab}n^{a}n^{b}< 0$ for a hypersurface orthogonal timelike $n^{a}$, at least over some portion of the region of interest of the manifold. This implies violation of the strong energy condition by the matter fields, the simplest example of which is a positive cosmological constant.