Violations of the Kerr and Reissner-Nordstrom bounds: horizon versus asymptotic quantities

TL;DR

This paper explores violations of the Kerr and Reissner-Nordstrom bounds in various black hole solutions, highlighting differences between horizon and asymptotic quantities, and proposes a new parameterization for black hole spacetimes.

Contribution

It demonstrates that well-known rotating and charged black holes violate the Kerr and Reissner-Nordstrom bounds in terms of horizon quantities and introduces a new parameterization approach for black hole spacetimes.

Findings

Kerr bound is violated in horizon quantities for Kerr BHs with scalar or Proca hair.

Reissner-Nordstrom bound is violated in horizon quantities even in the static limit.

Event horizon linear velocity remains below the speed of light in all cases.

Abstract

A central feature of the most elementary rotating black hole (BH) solution in General Relativity is the Kerr bound, which, for vacuum Kerr BHs, can be expressed either in terms of the ADM or the horizon "charges". This bound, however, is not a fundamental properties of General Relativity and stationary, asymptotically flat, regular (on and outside an event horizon) BHs are known to violate the Kerr bound, both in terms of their ADM and horizon quantities. Examples include the recently discovered Kerr BHs with scalar or Proca hair. Here, we point the fact that the Kerr bound in terms of horizon quantities is also violated by well-known rotating and charged solutions, known in closed form, such as the Kerr-Newman and Kerr-Sen BHs. For the former, moreover, we observe that the Reissner-Nordstrom (RN) bound is also violated in terms of horizon quantities, even in the static (i.e RN) limit. For the latter, by contrast, the existence of charged matter outside the horizon, allows a curious invariance of the charge to mass ratio, between ADM and horizon quantities. Regardless of the Kerr bound violation, we show that in all case, the event horizon linear velocity never exceeds the speed of light. Finally, we suggest a new type of informative parameterization for BH spacetimes where part of the asymptotic charges is supported outside the horizon.