On the Size of Rotating Black Holes

TL;DR

This paper extends inequalities relating black hole horizon, photon sphere, and shadow from static to rotating black holes, confirming their validity for various solutions and showing rotation reduces their sizes.

Contribution

It introduces a method to analyze the size parameters of rotating black holes and verifies the inequalities for multiple black hole solutions.

Findings

Inequalities hold for Kerr, Kerr-Newman, Kerr-Sen, and Kerr-Cvetic-Youm black holes.

Rotation decreases both the actual and apparent sizes of black holes.

Shadow shape varies with viewing angle, remaining round from the north pole.

Abstract

Recently a sequence of inequalities relating the black hole horizon, photon sphere, shadow were proposed for spherically symmetric and static black holes, providing the upper bound for given mass. In this paper, we extend the discussion to include rotating black holes. When viewed from the north pole direction, the shadow remains a round disk, but the image is skewed when viewed from the equatorial plane. After properly implementing the ``size'' parameters for the rotating black holes, we verify that the sequence of inequalities remain valid for a variety of solutions, including Kerr, Kerr-Newman, Kerr-Sen and Kerr-Cveti\v c-Youm black holes. The upshot is that rotation makes both the actual and apparent sizes of a black hole smaller.