No-Go Theorem in Spacetimes with Two Commuting Spacelike Killing Vectors

TL;DR

This paper proves that in certain four-dimensional spacetimes with specific symmetries, no outer apparent horizons can exist if the dominant energy condition is satisfied, highlighting limitations on black hole structures in these settings.

Contribution

It establishes a no-go theorem for outer apparent horizons in spacetimes with two commuting spacelike Killing vectors under Einstein's gravity.

Findings

No outer apparent horizons in these spacetimes.

The dominant energy condition is crucial for the theorem.

Constraints on black hole formation in symmetric spacetimes.

Abstract

Four-dimensional Riemannian spacetimes with two commuting spacelike Killing vectors are studied in Einstein's theory of gravity, and found that no outer apparent horizons exist, provided that the dominant energy condition holds.