Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects

TL;DR

This paper derives a universal charge-radius relation that limits the net charge of various subatomic and astrophysical objects based on electron-positron pair creation constraints, applicable across different size scales.

Contribution

It introduces a universal charge-radius relation for static, spherical objects, improving upon previous charge limits by incorporating quantum pair creation effects.

Findings

Universal relation $Z=0.71R_{fm}$ for radii 400 fm to 10,000 fm.

For larger radii, $Z=7 imes 10^{-5} R_{fm}^2$, applicable to astrophysical objects.

Relation matches known charge limits for nuclear density objects.

Abstract

Electron-positron pair creation in supercritical electric fields limits the net charge of any static, spherical object, such as superheavy nuclei, strangelets, and Q-balls, or compact stars like neutron stars, quark stars, and black holes. For radii between $4\times10^2$ fm and $10^4$ fm the upper bound on the net charge is given by the universal relation $Z=0.71R_{fm}$, and for larger radii (measured in fm or km) $Z = 7 \times 10^{-5} R_{fm}^2 = 7 \times 10^{31} R_{km}^2$. For objects with nuclear density the relation corresponds to $Z \approx 0.7 A^{1/3}$ ($10^{8} < A < 10^{12}$) and $Z \approx 7\times10^{-5} A^{2/3}$ ($A > 10^{12}$), where $A$ is the baryon number. For some systems this universal upper bound improves existing charge limits in the literature.