Observables for moving, extremely charged primordial extremely massive black holes

Frampton PLB 835 (2022) put forward the idea that charged, primordial extremely massive black holes between $10^{11}$ and $10^{22}$ solar masses could exist and may explain the observed accelerated expansion of the universe in lieu of dark energy. The extreme charge turns these black holes into naked singularities, making it difficult to derive observable signatures in their proximity. Here, we derive the electro-magnetic and gravitational lensing effects caused by such extreme objects at distances much larger than their extent and discuss the most promising observables to search for their existence in the least cosmology-dependent way. Restricting searches to black holes between $10^{12}$ to $10^{14}$ solar masses, we show that such objects do not cause any totally disruptive catastrophes, like dissociation of neutral hydrogen clouds or proton decay induced by strong electro-magnetic fields. Einstein rings of the order of 10 arcsec and rotation measures of plasma clouds subject to the magnetic fields induced by the black holes are identified as optimum observable signatures of these black holes in current sky surveys.