Universal lower bound on orbital periods

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}}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 }>{{2pi ehbar }over {sqrt{G}c^2 m^2_{e}}} (here E_{text {c}}=m^2_{e}/ehbar 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.