Black Holes are Neither Particle Accelerators Nor Dark Matter Probes

It has been suggested that maximally spinning black holes can serve as particle accelerators, reaching arbitrarily high center-of-mass energies. Despite several objections regarding the practical achievability of such high energies, and demonstrations past and present that such large energies could never reach a distant observer, interest in this problem has remained substantial. We show that, unfortunately, a maximally spinning black hole can never serve as a probe of high energy collisions, even in principle and despite the correctness of the original diverging energy calculation. Black holes can indeed facilitate dark matter annihilation, but the most energetic photons can carry little more than the rest energy of the dark matter particles to a distant observer, and those photons are actually generated relatively far from the black hole where relativistic effects are negligible. Therefore, any strong gravitational potential could probe dark matter equally well, and an appeal to black holes for facilitating such collisions is unnecessary.

Figure 1

Radial velocity of several null geodesics as viewed by an observer at infinity.

Figure 2

Escape fraction as a function of radius. Panel (a) shows the domain $1\le r\le 10$, whereas panel (b) shows a zoomed-in view of $1\le r\le 1.1$. Where the simple correction of a factor 2 plainly increases the escape fraction relative to Ref. 4 by 2 everywhere, the other corrections discussed in the text greatly diminish the escape fraction for $r\le 1.1$, so that our calculated escape fraction is several orders of magnitude below that calculated in Ref. 4 for small radii.

Figure 3

Contours of energy and flux for $0\le \ell \le 2$ and $1\le r\le 10$. Panel (a) shows the c.m. energy and panel (b) shows the energy measured at infinity versus the flux reaching an observer 10 kpc away, assuming the outgoing photon carries half of the collision energy.