The full integration of black hole solutions to symmetric supergravity theories

Authors:
  • WCW. Chemissany
    W. Chemissany
  • JRJ. Rosseel
    J. Rosseel
  • MTM. Trigiante
    M. Trigiante
  • TRT. Van Riet
    T. Van Riet
Preprint
Publisher website
Google Scholar
Abstract
We prove that all stationary and spherical symmetric black hole solutions to theories with symmetric target spaces are integrable and we provide an explicit integration method. This exact integration is based on the description of black hole solutions as geodesic curves on the moduli space of the theory when reduced over the timelike direction. These geodesic equations of motion can be rewritten as a specific Lax pair equation for which mathematicians have provided the integration algorithms when the initial conditions are described by a diagonalizable Lax matrix. We comment on BPS versus non-BPS extremal black holes in this setup. The explicit details, such as a full integration of the STU-model and the non-diagonalizable integration algorithm, is left for a future work and instead some simple examples to illustrate our point are presented.