Universal BPS structure of stationary supergravity solutions

Abstract

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 to 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 is identified as a Lagrangian subvariety of the variety of nilpotent elements of 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. * email address: bossard@aei.mpg.de † email address: Hermann.Nicolai@aei.mpg.de ‡ email address: k.stelle@imperial.ac.uk where the 'momentum' ǫ is the asymptotic supersymmetry parameter (Killing spinor)

Axion wormholes in AdS compactifications

“…This can be understood as follows: imagine that regular wormholes existed in these theories. This would mean, using the oxidation formulae in [14] (see also [16,17]), there are smooth, four-dimensional black holes in the original theory that violate the generalised Reissner-Nordstrom bound. However this was proven to be impossible [14].…”

An inverse scattering formalism for STU supergravity

“…The rank of the four-dimensional Schwarzschild solution for example in a theory with symmetry group G after reduction to three dimensions depends on the embedding of the standard Ehlers SL(2, R) representation into G. For the STU model with G = SO (4,4) this rank is two, for the theory with G = E 6 the rank is six and for maximal supergravity with G = E 8 the rank will be 57. For other cases of interest the rank can be obtained for instance from the analysis of appendix A of [21].…”

A general black string and its microscopics

“…The matrix Q is also called the charge matrix. In [32] it was observed, following [23], that the charge matrix Q for any four-dimensional asymptotically flat nonextremal axisymmetric solution satisfies…”