Built on

E. Cremmer and B. Julia, “The SO(8) Supergravity,” Nucl. Phys. B
1979
Earlier work this paper cites.
W. Hahn, “Stability of Motion,” Springer-Verlag, 1967; N. Rouche and J. Mawhin, “Ordinary Differential Equations. Stability and Periodic Solutions,” Pitman, Boston/London/Melbourne, 1980
1980
Earlier work this paper cites.
V. I. Arnold,“Mathematical Methods of Classical Mechanics” (Graduate Texts in Mathematics), Springer, 1997; K. Meyer, G. Hall, “Introduction to Hamiltonian Dynamical Systems and the N-Body Problem,” , Springer-Verlag, 1992
1992
Earlier work this paper cites.
R. Kallosh and B. Kol, “E(7) Symmetric Area of the Black Hole Horizon,” Phys. Rev. D
Original
1996
Earlier work this paper cites.
J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP
2003
Earlier work this paper cites.
D. Z. Freedman, C. Nunez, M. Schnabl and K. Skenderis, “Fake Supergravity and Domain Wall Stability,” Phys. Rev. D
2004
Earlier work this paper cites.

Similar

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Then

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2008
Later among the works it cites.
E. G. Gimon, F. Larsen and J. Simon, “Black Holes in Supergravity: the non-BPS Branch,” JHEP
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2008
Later among the works it cites.
B. L. Cerchiai, S. Ferrara, A. Marrani and B. Zumino, “Duality, Entropy and ADM Mass in Supergravity,” Phys. Rev. D
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Later among the works it cites.
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Original
2010
Closest in time.
G. Bossard, Y. Michel and B. Pioline, “Extremal black holes, nilpotent orbits and the true fake superpotential,” JHEP

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2010

Fake Superpotential for Large and Small Extremal Black Holes

Andrianopoli, L., D'Auria, R., Ferrara, S. et al.

Understand

We consider the fist order, gradient-flow, description of the scalar fields coupled to spherically symmetric, asymptotically flat black holes in extended supergravities.

Using the identification of the fake superpotential with Hamilton's characteristic function we clarify some of its general properties, showing in particular (besides reviewing the issue of its duality invariance) that W has the properties of a Liapunov's function, which implies that its extrema (associated with the horizon of extremal black holes) are asymptotically stable equilibrium points of the corresponding first order dynamical system (in the sense of Liapunov).
Moreover, we show that the fake superpotential W has, along the entire radial flow, the same flat directions which exist at the attractor point.
This allows to study properties of the ADM mass also for small black holes where in fact W has no critical points at finite distance in moduli space.

Built on

E. Cremmer and B. Julia, “The SO(8) Supergravity,” Nucl. Phys. B
1979
Earlier work this paper cites.
W. Hahn, “Stability of Motion,” Springer-Verlag, 1967; N. Rouche and J. Mawhin, “Ordinary Differential Equations. Stability and Periodic Solutions,” Pitman, Boston/London/Melbourne, 1980
1980
Earlier work this paper cites.
V. I. Arnold,“Mathematical Methods of Classical Mechanics” (Graduate Texts in Mathematics), Springer, 1997; K. Meyer, G. Hall, “Introduction to Hamiltonian Dynamical Systems and the N-Body Problem,” , Springer-Verlag, 1992
1992
Earlier work this paper cites.
R. Kallosh and B. Kol, “E(7) Symmetric Area of the Black Hole Horizon,” Phys. Rev. D
Original
1996
Earlier work this paper cites.
J. de Boer, E. P. Verlinde and H. L. Verlinde, “On the holographic renormalization group,” JHEP
2003
Earlier work this paper cites.
D. Z. Freedman, C. Nunez, M. Schnabl and K. Skenderis, “Fake Supergravity and Domain Wall Stability,” Phys. Rev. D
2004
Earlier work this paper cites.