Upper Bound for Diameter of Cosmological Black Holes and Nonexistence of Black Strings

TL;DR

This paper establishes an upper bound on the apparent horizon diameter in spacetimes with a positive cosmological constant and argues that infinitely long black strings cannot form in our universe.

Contribution

It provides a rigorous upper bound for the apparent horizon diameter in such spacetimes and demonstrates the nonexistence of infinitely long black strings.

Findings

Maximum apparent horizon diameter is $2\pi/\sqrt{3\varLambda}$.

Black strings cannot be arbitrarily long in our universe.

Supports stability and uniqueness of black hole horizons in positive cosmological constant spacetimes.

Abstract

The diameter of the apparent horizon, defined by the distance between furthest points on the horizon, in spacetimes with a positive cosmological constant $\varLambda$ has been investigated. It is established that the diameter of the apparent horizon on the totally umbilic partial Cauchy surface cannot exceed $2\pi/\sqrt{3\varLambda}$. Then, it is argued that arbitrarily long black strings cannot be formed in our universe.