Journal of High Energy Physics

, 2019:90 | Cite as

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

  • Alex Giacomini
  • Marcello OrtaggioEmail author
Open Access
Regular Article - Theoretical Physics


We consider a class of ansätze for the construction of exact solutions of the Einstein-nonlinear σ-model system with an arbitrary cosmological constant in (3+1) dimensions. Exploiting a geometric interplay between the SU(2) field and Killing vectors of the spacetime reduces the matter field equations to a single scalar equation (identically satisfied in some cases) and simultaneously simplifies Einstein’s equations. This is then exemplified over various classes of spacetimes, which allows us to construct stationary black holes with a NUT parameter and uniform black strings, as well as time-dependent solutions such as Robinson-Trautman and Kundt spacetimes, Vaidya-type radiating black holes and certain Bianchi IX cosmologies. In addition to new solutions, some previously known ones are rederived in a more systematic way.


Black Holes Sigma Models 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Ciencias Físicas y MatemáticasUniversidad Austral de ChileValdiviaChile
  2. 2.Institute of Mathematics of the Czech Academy of SciencesPrague 1Czech Republic

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