Two mass conjectures on axially symmetric black hole--disk systems

TL;DR

This paper investigates mass bounds in axially symmetric black hole--disk systems, providing numerical evidence and analytical proofs for limits on system mass based on rotation laws and spacetime properties.

Contribution

It introduces new mass conjectures for black hole--disk systems and proves a specific bound analytically for massless dust disks in Kerr spacetime.

Findings

Numerical evidence supports mass bounds related to angular velocity and momenta.

Analytical proof established for massless dust disks in Kerr spacetime.

Proposes general-relativistic Keplerian rotation law as a key factor.

Abstract

We analyze stationary self-gravitating disks around spinning black holes that satisfy the recently found general-relativistic Keplerian rotation law. There is a numerical evidence that the angular velocity, circumferential radius and angular momenta yield a bound onto the asymptotic mass of the system. This bound is proven analytically in the special case of massless disks of dust in the Kerr spacetime.