Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects

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 $4\times {10}^2$ 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) $Z = 7 \times 10^{-5} R_{fm}^2 = 7 \times 10^{31} R_{km}^2$\mathrm{.}Forobjectswithnucleardensitytherelationcorrespondsto$Z \approx 0.7 A^{1/3}$($10^{8} < A < 10^{12}$)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.