Introducing the inverse hoop conjecture for black holes

TL;DR

This paper proposes and proves a new inverse hoop conjecture relating black hole surface area and circumference, demonstrating its validity for Kerr-Newman-(anti)-de Sitter black holes.

Contribution

It introduces the inverse hoop conjecture for black holes and provides a proof for Kerr-Newman-(anti)-de Sitter solutions, expanding understanding of black hole geometry.

Findings

Black holes satisfy the inverse hoop relation ${ m A} \, \leq \, {\cal C}^2/\pi$

The conjecture holds for Kerr-Newman-(anti)-de Sitter black holes

Provides a geometric inequality linking area and circumference in black hole physics.

Abstract

It is conjectured that stationary black holes are characterized by the inverse hoop relation ${\cal A}\leq {\cal C}^2/\pi$, where ${\cal A}$ and ${\cal C}$ are respectively the black-hole surface area and the circumference length of the smallest ring that can engulf the black-hole horizon in every direction. We explicitly prove that generic Kerr-Newman-(anti)-de Sitter black holes conform to this conjectured area-circumference relation.