2009/02/28 by Guillaume Bossard, Hermann Nicolai, K. S. Stelle +1 · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/07/003
published as JHEP 0907:003,2009 · Few misprints corrected
openalex publication_date 2009/07/01 · arxiv created 2009/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H* pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C > of Spin*(2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C>. The invariance of a given solution with respect to supersymmetry is determined by an algebraic `Dirac equation' on the Weyl spinor |C>. We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub-NUT black holes with respect with their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H*-orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes as a Lagrangian subvariety of the variety of nilpotent elements of Lie(G). We also generalise the notion of active duality transformations to an `almost action' of the three-dimensional duality group G on asymptotically flat stationary solutions.