On Extremal Limits and Duality Orbits of Stationary Black Holes

Abstract

With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting global symmetry orbits (duality orbits) of non-extremal solutions to those of extremal black holes. We focus our attention on a generic representative of these orbits, providing its explicit description in terms of D=4 fields. As a byproduct, using a new characterization of the angular momentum in terms of quantities intrinsic to the geometry of the D=3 effective model, we are able to prove on general grounds its invariance, as a function of the boundary data, under the D=4 global symmetry. In the extremal under-rotating limit it becomes moduli-independent. We also discuss the issue of the fifth parameter characterizing the four-dimensional seed solution, showing that it can be generated by a transformation in the global symmetry group which is manifest in the D=3 effective description.

24 pages, LaTeX source, typos corrected, expressions for the entropy of the non-extremal solutions added

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• Constructing black hole solutions in supergravity theories
• Supersymmetric smooth distributions of M2-branes as AdS solitons
• Geroch Group Description of Black Holes
• Exact holographic RG flows in extended SUGRA
• Nilpotent orbits in real symmetric pairs and stationary black holes
• Entropy of non-extremal STU black holes: the F-invariant unveiled
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits