Maximum magnetic moment to angular momentum conjecture

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-WilsonBlackett number, cµ/JG 1 2 , where µ 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.

Stationary double black hole without naked ring singularity

“…The ratio |µ/J| is bounded above by 1/5, in agreement with the Barrow-Gibbons bound [48] |µ/J| ≤ 1, while the ratio |J|/M 2 satisfies the Kerr-like bound…”

The essence of the Blandford–Znajek process

“…Note that h µν is the induced metric on the field sheet and N µ ν is the projection tensor onto directions normal to the field sheet. The former equation (11) describes dynamics of field sheets acted on by a force associated with B, i.e., magnetic pressure; the latter equation (12) does conservation of the magnetic flux. This expression tells us that the dynamics of field sheets in FFE is similar to the dynamics of world sheets for Nambu-Goto strings.…”

“…Comparing the above equation with Eqs. (11) and (12), we can easily notice that the only difference between the dynamics of field sheets and world sheets is the addition of the extra scalar quantity B, which describes the magnetic tension and pressure. (In the flat spacetime such a correspondence was discussed in Refs.…”

“…* Electronic address: kinoshita@phys.chuo-u.ac.jp † Electronic address: igata@rikkyo.ac.jp 1 For historical details, see Ref. [11].…”

From Maximal Force to the Field Equations of General Relativity

“…The oldest publications known to the authors are by Rauscher [5] and by Treder [6] and suggested the value c 4 /G as upper bound. More recent publications that focused specifically on the topic of the upper bound derived the value c 4 /4G, including those of Gibbons [2], Schiller [3], and Barrow and Gibbons [7,8]. Therefore we keep the factor 4 in the denominator.…”