Gravitational shockwaves on rotating black holes

We present an exact solution of Einstein's equation that describes the gravitational shockwave of a massless particle on the horizon of a Kerr-Newman black hole. The backreacted metric is of the generalized Kerr-Schild form and is Type II in the Petrov classification. We show that if the background frame is aligned with shear-free null geodesics, and if the background Ricci tensor satisfies a simple condition, then all nonlinearities in the perturbation will drop out of the curvature scalars. We make heavy use of the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).Comment: v4: Substantially shortened (45 pages). Major casualties: Point-particle limit of field theory and over 100 footnotes. Minor casualties: Detailed exposition of background material. Corrections: Formal redefinition of Ricci and energy scalars from traceless tensors, note about extrinsic curvature, a stray prime, some numerical factors. No results were harmed. v5: Minor edits. v6: Publishe

The Origin of Families and SO(18)SO(18) Grand Unification

We exploit a recent advance in the study of topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa couplings of intermediate strength may allow the mirror matter and extra families to decouple at arbitrarily high energies. As was clear from the existing literature, we have to go beyond the Higgs mechanism in order to solve the family puzzle. A pattern of symmetry breaking which results in the SU(5) grand unified theory with horizontal or family symmetry USp(4) = Spin(5) (or more loosely, SO(5)) leaves exactly three light families of matter and seems particularly appealing. We comment briefly on an alternative scheme involving discrete non-abelian family symmetries. In a few lengthy appendices we review some of the pertinent condensed matter theory.Comment: 31 pages, no figures. v2: minor changes, added subsection II.