Critical gravitational inspiral of two massless particles

Abstract

If two ultrarelativistic nonrotating black holes of masses \(m_1\) and \(m_2\) approach each other with fixed center-of-momentum (COM) total energy \(E = \sqrt{s} \gg (m_1+m_2)c^2\) that has a corresponding Schwarzschild radius \(R = 2GE/c^4\) much larger than the Schwarzschild radii of the individual black holes, here it is conjectured that at the critical impact parameter \(b_c\) between scattering and coalescing into a single black hole, there will be an inspiral of many orbital rotations for \(m_1c^2/E \ll 1\) and \(m_2c^2/E \ll 1\) before a final black hole forms, during which all of the initial kinetic energy will be radiated away in gravitational waves by the time the individual black holes coalesce and settle down to a stationary state. In the massless limit \(m_1 = m_2 = 0\), in which the black holes are replaced by classical massless point particles, it is conjectured that for the critical impact parameter, all of the total energy will be radiated away by the time the two particle worldlines merge and end. One might also conjecture that in the limit of starting with the massless particles having infinite energy in the infinite past with the correct ratio of impact parameter to energy, the spacetime for retarded time before the final worldline merger at zero energy will have a homothetic vector field and hence be self similar. Evidence against these conjectures is also discussed, and if it proves correct, I conjecture that two massless particles can form any number of black holes.