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P. Breitenlohner, G. W. Gibbons, D. Maison, Four-Dimensional Black Holes from Kaluza-Klein Theories
1988
Earlier work this paper cites.
A. Strominger, Special Geometry
1990
Earlier work this paper cites.
B. de Wit, F. Vanderseypen, A. Van Proeyen, Symmetry structure of special geometries
1993
Earlier work this paper cites.
D. Rasheed, The Rotating dyonic black holes of Kaluza-Klein theory
1995
Earlier work this paper cites.
M. J. Duff, J. T. Liu and J. Rahmfeld, Four-dimensional String-String-String Triality
1996
Earlier work this paper cites.
A. Ceresole, R. D’Auria and S. Ferrara, The Symplectic Structure of N = 2 \mathit{N=2} Supergravity and Its Central Extension
1996
Earlier work this paper cites.
S. Ferrara and R. Kallosh, Supersymmetry and Attractors
1996
Earlier work this paper cites.
S. Ferrara, G. W. Gibbons and R. Kallosh, Black holes and critical points in moduli space
1997
Earlier work this paper cites.
L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré and T. Magri, N = 2 \mathit{N=2} Supergravity and N = 2 \mathit{N=2} Super Yang-Mills Theory on General Scalar Manifolds : Symplectic Covariance, Gaugings and the Momentum Map
1997
Earlier work this paper cites.
F. Denef, Supergravity flows and D \mathit{D} -brane stability
2000
Earlier work this paper cites.
F. Larsen, Rotating Kaluza-Klein black holes
2000
Earlier work this paper cites.

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2007
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S. Ferrara and A. Marrani, On the Moduli Space of non-BPS Attractors for N = 2 \mathit{N=2} Symmetric Manifolds
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S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, 𝑠𝑡𝑢 \mathit{stu} Black Holes Unveiled
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2008
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K. Goldstein and S. Katmadas, Almost BPS black holes
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2009
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Then

A. Ceresole, G. Dall’Agata, S. Ferrara and A. Yeranyan, First order flows for N = 2 \mathit{N=2} extremal black holes and duality invariants
Original
2010
Later among the works it cites.
I. Bena, S. Giusto, C. Ruef and N. P. Warner, Supergravity solutions from floating branes
Original
2011
Later among the works it cites.
P. Galli and J. Perz, Non-supersymmetric extremal multicenter black holes with superpotentials
Original
2011
Later among the works it cites.
B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites
2011
Later among the works it cites.
A. Ceresole, S. Ferrara, A. Marrani and A. Yeranyan, Small Black Hole Constituents and Horizontal Symmetry
Original

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2012

Multi-Centered First Order Formalism

Ferrara, Sergio, Marrani, Alessio, Shcherbakov, Andrey et al.

Understand

We propose a first order formalism for multi-centered black holes with flat tree-dimensional base-space, within the stu model of N=2, D=4 ungauged Maxwell-Einstein supergravity.

This provides a unified description of first order flows of this universal sector of all models with a symmetric scalar manifold which can be obtained by dimensional reduction from five dimensions.
We develop a D=3 Cartesian formalism which suitably extends the definition of central and matter charges, as well as of black hole effective potential and first order "fake" superpotential, in order to deal with not necessarily axisimmetric solutions, and thus with multi-centered and/or (under-)rotating extremal black holes.
We derive general first order flow equations for composite non-BPS and almost BPS classes, and we analyze some of their solutions, retrieving various single-centered (static or under-rotating) and multi-centered known systems.

Built on

P. Breitenlohner, G. W. Gibbons, D. Maison, Four-Dimensional Black Holes from Kaluza-Klein Theories
1988
Earlier work this paper cites.
A. Strominger, Special Geometry
1990
Earlier work this paper cites.
B. de Wit, F. Vanderseypen, A. Van Proeyen, Symmetry structure of special geometries
1993
Earlier work this paper cites.
D. Rasheed, The Rotating dyonic black holes of Kaluza-Klein theory
1995
Earlier work this paper cites.
M. J. Duff, J. T. Liu and J. Rahmfeld, Four-dimensional String-String-String Triality
1996
Earlier work this paper cites.
A. Ceresole, R. D’Auria and S. Ferrara, The Symplectic Structure of N = 2 \mathit{N=2} Supergravity and Its Central Extension
1996
Earlier work this paper cites.
S. Ferrara and R. Kallosh, Supersymmetry and Attractors
1996
Earlier work this paper cites.
S. Ferrara, G. W. Gibbons and R. Kallosh, Black holes and critical points in moduli space
1997
Earlier work this paper cites.
L. Andrianopoli, M. Bertolini, A. Ceresole, R. D’Auria, S. Ferrara, P. Fré and T. Magri, N = 2 \mathit{N=2} Supergravity and N = 2 \mathit{N=2} Super Yang-Mills Theory on General Scalar Manifolds : Symplectic Covariance, Gaugings and the Momentum Map
1997
Earlier work this paper cites.
F. Denef, Supergravity flows and D \mathit{D} -brane stability
2000
Earlier work this paper cites.
F. Larsen, Rotating Kaluza-Klein black holes
2000
Earlier work this paper cites.