Rotating black holes, global symmetry and first order formalism

Abstract

In this paper we consider axisymmetric black holes in supergravity and address the general issue of defining a first order description for them. The natural setting where to formulate the problem is the De Donder-Weyl-Hamilton-Jacobi theory associated with the effective two-dimensional sigma-model action describing the axisymmetric solutions. We write the general form of the two functions S_m defining the first-order equations for the fields. It is invariant under the global symmetry group G_(3) of the sigma-model. We also discuss the general properties of the solutions with respect to these global symmetries, showing that they can be encoded in two constant matrices belonging to the Lie algebra of G_(3), one being the Noether matrix of the sigma model, while the other is non-zero only for rotating solutions. These two matrices allow a G_(3)-invariant characterization of the rotational properties of the solution and of the extremality condition. We also comment on extremal, under-rotating solutions from this point of view.

26 pages, LaTeX source

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• On Extremal Limits and Duality Orbits of Stationary Black Holes
• Black string first order flow in N=2, d=5 abelian gauged supergravity
• Extremal Limits of Rotating Black Holes
• Constructing black hole solutions in supergravity theories
• Nilpotent orbits in real symmetric pairs and stationary black holes
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
• Multi-Centered First Order Formalism