Particle Accelerators inside Spinning Black Holes

On the basis of the Kerr metric as a model for a spinning black hole accreting test particles from rest at infinity, I show that the center-of-mass energy for a pair of colliding particles is generically divergent at the inner horizon. This shows not only that classical black holes are internally unstable, but also that Planck-scale physics is a characteristic feature within black holes at scales much larger that the Planck length. The novel feature of the divergence discussed here is that the phenomenon is present only for black holes with rotation, and in this sense it is distinct from the well-known Cauchy horizon instability.

Figure 1

The roots $L$ along with $A$ for comparison. The purpose of this diagram is to show that our choice for the range $L_2<l_2<L_1$ excludes the fine-tuning $l_2=A$ characteristic of the BSW mechanism.

Figure 2

A sketch of the function $W$ (shown for $a=0.95$) with details in the insert. The roots $L$ are shown. The purpose of this diagram is to show that our choice for the range $L_4<l_1<L_3$ does not require counterstreaming, that is, $l_1<0$.

Figure 3

A plot of $N_{-}$, given by (9), for $a=0.95$ within the stated ranges for $l_1$ and $l_2$. Other plots in the range $0<a<1$ are qualitatively similar. The purpose of this diagram is to show that $N_{-}$ does not evaluate to 0 generically.