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

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 Arnowitt-Deser-Misner (ADM) or horizon "charges." However, this bound is not a fundamental property of general relativity and stationary, asymptotically flat, and regular (on and outside an event horizon) BHs are known to violate the Kerr bound, in terms of both their ADM and horizon quantities. Examples include the recently discovered Kerr BHs with scalar [C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)] or Proca hair [C. Herdeiro, E. Radu, and H. Runarsson, arXiv: 1603.02687]. Here, we point out the fact that the Kerr bound in terms of horizon quantities is also violated by well-known rotating and charged solutions which are known in closed form, such as the Kerr-Newman and Kerr-Sen BHs. Moreover, for the former we observe that the Reissner-Nordstrom (RN) bound is also violated in terms of horizon quantities, even in the static (i.e., RN) limit. By contrast, for the latter the existence of charged matter outside the horizon allows for a curious invariance of the charge-to-mass ratio between the ADM and horizon quantities. Regardless of the Kerr bound violation, we show that in all cases the event horizon linear velocity [C. A. R. Herdeiro and E. Radu, Int. J. Mod. Phys. D 24, 1544022 (2015)] never exceeds the speed of light. Finally, we suggest a new type of informative parametrization for BH spacetimes where part of the asymptotic charge is supported outside the horizon.