Destroying a near-extremal Kerr-Newman black hole

We revisit here a previous argument due to Wald showing the impossibility of turning an extremal Kerr-Newman black hole into a naked singularity by plunging test particles across the black hole event horizon. We extend Wald’s analysis to the case of near-extremal black holes and show that it is indeed possible to destroy their event horizon, giving rise to naked singularities, by pushing test particles toward the black hole as, in fact, it has been demonstrated explicitly by several recent works. Our analysis allows us to go a step further and to determine the optimal values, in the sense of keeping to a minimum the backreaction effects, of the test particle electrical charge and angular momentum necessary to destroy a given near-extremal Kerr-Newman black hole. We describe briefly a possible realistic scenario for the creation of a Kerr naked singularity from some recently discovered candidates to be rapidly rotating black holes in radio galaxies.

Figure 1

The effective potential (18) for a test particle with angular momentum $L$ and rest mass $\mu$ around an extremal Kerr black hole with mass $M$. For this figure, $L/M^2={10}^{-5}$ and $\mu /M={10}^{-6}$ (a), $2.5\times {10}^{-6}$ (b), $5\times {10}^{-6}$ (c), $7.5\times {10}^{-6}$ (d), and ${10}^{-5}$ (e). The dotted horizontal line corresponds to the value of the effective potential at the black-hole horizon ($E_{\min }$), which does not dependent on $\mu$.