# A maximum magnetic moment to angular momentum conjecture

## TL;DR

This paper proposes a new conjecture that the ratio of magnetic moment to angular momentum in nature is bounded by a value of order unity, supported by checks against various black hole solutions.

## Contribution

Introduces a novel conjecture bounding the dimensionless ratio of magnetic moment to angular momentum, with verification across multiple black hole models in different theories.

## Key findings

- The conjecture holds for charged rotating black holes in Einstein-Maxwell, Kaluza-Klein, Kerr-Sen, and supergravity theories.
- Supports the conjecture with exact solutions in various gravitational theories.
- Discusses the relation to other fundamental bounds like the Maximum Tension and Dyson Luminosity.

## Abstract

Conjectures play a central role in theoretical physics, especially those that assert an upper bound to some dimensionless ratio of physical quantities. In this paper we introduce a new such conjecture bounding the ratio of the magnetic moment to angular momentum in nature. We also discuss the current status of some old bounds on dimensionless and dimensional quantities in arbitrary spatial dimension. Our new conjecture is that the dimensionless Schuster-Wilson-Blackett number, c{\mu}/JG^{(1/2)}, where {\mu} is the magnetic moment and J is the angular momentum, is bounded above by a number of order unity. We verify that such a bound holds for charged rotating black holes in those theories for which exact solutions are available, including the Einstein-Maxwell theory, Kaluza-Klein theory, the Kerr-Sen black hole, and the so-called STU family of charged rotating supergravity black holes. We also discuss the current status of the Maximum Tension Conjecture, the Dyson Luminosity Bound, and Thorne's Hoop Conjecture.