Gravitational shockwaves on rotating black holes

  • Yoni BenTovEmail author
  • Joe Swearngin
Research Article


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).


Exact solution Rotating black hole Differential geometry General relativity Kerr-Newman metric Dray–’t Hooft Gravitational shockwave Newman–Penrose formalism Geroch–Held–Penrose formalism 



We thank Jan Willem Dalhuisen, Aaron Zimmerman, David Nichols, Christopher White, Dave Aasen, Nick Hunter-Jones, Alex Rasmussen, Yonah Lemonik, Douglas Stanford, and Saul Teukolsky for insightful discussions at various points in this endeavor. Y. B. especially thanks Justin Wilson, Leo Stein, and Alexei Kitaev. J. S. especially thanks Dirk Bouwmeester. Y. B. is funded by the Institute for Quantum Information and Matter (NSF Grant PHY-1125565) with support from the Simons Foundation (Award No. 376205). J. S. is funded by a UCSB Central Fellowship.


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Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Institute for Quantum Information and MatterCalifornia Institute of TechnologyPasadenaUSA
  3. 3.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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