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

Constructing a class of topological solitons in magnetohydrodynamics

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t \in \mathbb{Z}^+$ and $n_p=1$ these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with infinite conductivity. Furthermore, we extend our stability analysis by considering a plasma with finite conductivity and estimate the soliton lifetime in such a medium as a function of the toroidal winding number.Comment: 5 pages, 3 figure

Conformal Cyclic Cosmology Signatures and Anomalies of the CMB Sky

Circles of low-variance and Hawking points in the Cosmic Microwave Background (CMB), resulting from black hole mergers and black hole evaporation, respectively, in a previous cycle of the universe, have been predicted as possible evidence for the Conformal Cyclic Cosmology model (CCC) introduced by R. Penrose. We present a high-resolution search for such low-variance circles in the Planck and WMAP CMB data, and introduce HawkingNet, our machine learning open-source software based on a ResNet18 algorithm, to search for Hawking points in the CMB. We find that CMB anomalies, consisting of a few bright pixels, erroneously lead to regions with many low-variance circles, and consequently sets of concentric low-variance circles, when applying the search criteria used in previous work [V.G. Gurzadyan, R. Penrose]. After removing the anomalies from the data no statistically significant low-variance circles can be found. Concerning Hawking points, also no statistically significant evidence is found when using a Gaussian temperature amplitude model over 1 degree opening angle and after accounting for CMB anomalies. That CMB anomalies themselves might be remnants of Hawking points is not supported by low-variance and/or low-temperature circles around them. The absence of such statistically-significant distinct features in the currently available CMB data does not disprove the CCC model but implies that higher resolution CMB data and/or refined CCC based predictions are needed to pursue the search for CCC signatures.Comment: prepared for JCAP rev