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 Nöther 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.

Rotating black holes, global symmetry and first order formalism / Andrianopoli, Laura Maria; Riccardo, D’Auria; Giaccone, Paolo; Trigiante, Mario. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - ELETTRONICO. - 2012:12(2012), pp. 0-29. [10.1007/JHEP12(2012)078]

Rotating black holes, global symmetry and first order formalism

ANDRIANOPOLI, Laura Maria;GIACCONE, PAOLO;TRIGIANTE, MARIO
2012

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 Nöther 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2505616
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