Universal lower bound on orbital periods around central compact objects

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 $ME_{\text{c}}\gg1$ 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: $T_{\infty}>{{2\pi e\hbar}\over{\sqrt{G}c^2 m^2_{e}}}$ (here $E_{\text{c}}=m^2_{e}/e\hbar$ is the critical electric field for pair production). The explicit dependence of the bound on the fundamental constants of nature $\{G,c,\hbar\}$ suggests that it may reflect a fundamental physical property of the elusive quantum theory of gravity.