Crystal Spacetimes with Discrete Translational Symmetry

  • Jiří Ryzner
  • Martin Žofka
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


The aim of this work is to construct exact solutions of Einstein–Maxwell(-dilaton) equations possessing a discrete translational symmetry. We present two approaches to the problem. The first one is to solve Einstein–Maxwell equations in 4D, the second one relies on dimensional reduction from 5D. We examine the geometry of the solutions, their horizons and singularities and compare them.


Majumdar–Papapetrou Extreme black hole Einstein–Maxwell solutions Scalar field Discrete symmetry 

Mathematics Subject Classification (2000)

83C15 83C22 83C57 



J.R. was supported by grant No. 80918 of Charles University Grant Agency. M.Ž. Acknowledges support by GACR 17-13525S.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jiří Ryzner
    • 1
  • Martin Žofka
    • 1
  1. 1.Institute of Theoretical PhysicsCharles UniversityPragueCzech Republic

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