We show that the second order field equations characterizing extremal solutions for spherically symmetric, stationary black holes are in fact implied by a system of first order equations given in terms of a prepotential W. This confirms and generalizes the results in \cite{anna}. Moreover we prove that the squared prepotential function shares the same properties of a c-function and that it interpolates between M2ADM and M2BR, the parameter of the near-horizon Bertotti-Robinson geometry. When the black holes are solutions of extended supergravities we are able to find an explicit expression for the prepotentials, valid at any radial distance from the horizon, which reproduces all the attractors of the four dimensional N>2 theories. Far from the horizon, however, for N-even, our ansatz poses a constraint on one of the U-duality invariants for the non-BPS solutions with Z≠0. We discuss a possible extension of our considerations to the non extremal case.
First order description of black holes in moduli space / Andrianopoli, Laura Maria; D'Auria, Riccardo; Orazi, Emanuele; Trigiante, Mario. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2007:11(2007). [10.1088/1126-6708/2007/11/032]
First order description of black holes in moduli space
ANDRIANOPOLI, Laura Maria;D'AURIA, RICCARDO;ORAZI, EMANUELE;TRIGIANTE, MARIO
2007
Abstract
We show that the second order field equations characterizing extremal solutions for spherically symmetric, stationary black holes are in fact implied by a system of first order equations given in terms of a prepotential W. This confirms and generalizes the results in \cite{anna}. Moreover we prove that the squared prepotential function shares the same properties of a c-function and that it interpolates between M2ADM and M2BR, the parameter of the near-horizon Bertotti-Robinson geometry. When the black holes are solutions of extended supergravities we are able to find an explicit expression for the prepotentials, valid at any radial distance from the horizon, which reproduces all the attractors of the four dimensional N>2 theories. Far from the horizon, however, for N-even, our ansatz poses a constraint on one of the U-duality invariants for the non-BPS solutions with Z≠0. We discuss a possible extension of our considerations to the non extremal case.File | Dimensione | Formato | |
---|---|---|---|
9227_UPLOAD.pdf
accesso aperto
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
PUBBLICO - Tutti i diritti riservati
Dimensione
276.87 kB
Formato
Adobe PDF
|
276.87 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/1653613