Eur. Phys. J. C (2023) 83: 655
https://doi.org/10.1140/epjc/s10052-023-11844-w

Letter

Universal lower bound on orbital periods

¹ The Ruppin Academic Center, 40250, Emeq Hefer, Israel
² The Hadassah Academic College, 91010, Jerusalem, Israel

^a shaharhod@gmail.com

Received: 1 June 2023
Accepted: 13 July 2023
Published online: 24 July 2023

Abstract

It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods $T_{\infty }$ of test particles around central compact objects as measured by flat-space asymptotic observers are fundamentally bounded from below. The lower bound on orbital periods becomes universal (independent of the mass M of the central compact object) in the dimensionless $M{E}_{\text{c}}\gg 1$ regime, in which case it can be expressed in terms of the electric charge e and the proper mass $m_e$ of the lightest charged particle in nature: $T_{\infty }>\frac{2\pi eħ}{\sqrt{G}{c}^2{m}_e^2}$ (here $E_{\text{c}}=m_e^2/eħ$ is the critical electric field for pair production). The explicit dependence of the bound on the fundamental constants of nature $\{G,c,ħ\}$ suggests that it may reflect a fundamental physical property of the elusive quantum theory of gravity.