quantity

charge to mass ratio

A dimensionless quantity comparing an object's electric charge to its mass, used to characterize black holes.
45 related articles · 1 formulas

Description

The charge-to-mass ratio is a fundamental property of any charged object, defined as its electric charge divided by its mass. For black holes, this ratio is a key parameter in the Reissner-Nordström and Kerr-Newman solutions of general relativity, determining the structure of the event horizon and the geometry of spacetime around the black hole. It influences how the black hole interacts with electromagnetic fields and how it emits radiation.

History

The concept of charge-to-mass ratio was first measured for the electron by J.J. Thomson in 1897. For black holes, the charged solutions were found by Hans Reissner and Gunnar Nordström in the 1910s, and later generalized to rotating charged black holes by Roy Kerr and Ezra Newman in the 1960s.

How it works

In classical physics, the charge-to-mass ratio determines how a particle responds to electric and magnetic fields. For a black hole, this ratio is set by the total charge and mass it has accumulated. A higher ratio means the black hole's electrostatic repulsion is stronger relative to its gravitational pull, which can lead to the existence of multiple horizons or even a naked singularity if the ratio exceeds a critical value.

In practice

In astrophysics, measuring the charge-to-mass ratio of black holes helps test general relativity and constrain models of black hole formation and evolution.

Fun fact

A black hole with a charge-to-mass ratio exceeding one would theoretically expose its singularity, a scenario known as a naked singularity, which is forbidden by the cosmic censorship conjecture.

Concept graph →

Formulas

$$\kappa = \frac{\Delta a / g}{\Delta (q/m)}$$
Relates acceleration difference to charge-to-mass ratio difference.
What is in the formula
κvariablesensitivity coefficient
Δavariabledifference in acceleration — acceleration metre per second squared
gvariablegravitational acceleration — gravitational acceleration metre per second squared
Δ(q/m)variabledifference in charge-to-mass ratio — charge to mass ratio coulomb per kilogram

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