The Problem of a Primordial Black Hole Hydrogenlike Atom

Abstract

It is shown that the recently proposed system composed of an electron and a primordial black hole forming a hydrogenlike atomic system cannot be stable, because the radiation pressure acting on the electron from Hawking radiation of the black hole far exceeds the binding force. On the contrary, if the black hole has a zero Hawking temperature, either due to its charge or spin, the required values of these parameters are so large that the electron would still not be stably bound to the black hole. However, if the black hole has a magnetic moment due to its spin, then electrons passing by the black hole could have spin-flip transitions producing high-energy gamma rays of ~1014 eV − 1015 eV.