Charged black hole remnants at the LHC

Abstract

We investigate possible signatures of long-lived (or stable) charged black holes at the Large Hadron Collider. In particular, we find that black hole remnants are characterised by quite low speed. Due to this fact, the charged remnants could, in some cases, be very clearly distinguished from the background events, exploiting dE/dX measurements. We also compare the estimate energy released by such remnants with that of typical Standard Model particles, using the Bethe–Bloch formula.

Appendix: Charged remnant BHs in the brane-world

A simple application of the four-dimensional Reissner–Nordström metric to BHs with mass $M\sim M_{\rm G}$ and charge Q∼e would show that such objects must be naked singularities. However, in brane-world models, one can employ the tidal charge form of the metric and find that, provided the tidal charge q is strong enough, microscopic BH can carry a charge of the order of e [47]. In particular, the horizon radius is now given by

(A.1)

where $M_{\rm P}$ and $\ell_{\rm P}$ are the Planck mass and length, respectively, and $\tilde{Q}$ is the electric charge in dimensionless units, that is,

(A.2)

Reality of Eq. (A.1) for a remnant of charge Q=±e and mass $M\simeq M_{\rm G}$ then requires

(A.3)

Configurations satisfying the above bound were recently found in Refs. [48, 49].