15 research outputs found
The extremal black holes of N=4 supergravity from so(8,2+n) nilpotent orbits
We consider the stationary solutions of N=4 supergravity coupled to n vector
multiplets that define linear superpositions of non-interacting extremal black
holes. The most general solutions of this type are derived from the graded
decompositions of so(8,2+n) associated to its nilpotent orbits. We illustrate
the formalism by giving explicitly asymptotically Minkowski non-BPS solutions
of the most exotic class depending on 6+n harmonic functions.Comment: Corrected version for publication, references adde
Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
We study the conditions of marginal stability for two-center extremal black
holes in N-extended supergravity in four dimensions, with particular emphasis
on the N=8 case. This is achieved by exploiting triangle inequalities satisfied
by matrix norms. Using different norms and relative bounds among them, we
establish the existence of marginal stability and split attractor flows both
for BPS and some non-BPS solutions. Our results are in agreement with previous
analysis based on explicit construction of multi-center solutions.Comment: 1+15 pages; v2: some new formulas added and misprints corrected; v3:
typos fixed, various refinements, Sec. 2.4 rewritten; to appear on JHE
Duality covariant non-BPS first order systems
We study extremal black hole solutions to four dimensional N=2 supergravity
based on a cubic symmetric scalar manifold. Using the coset construction
available for these models, we define the first order flow equations implied by
the corresponding nilpotency conditions on the three-dimensional scalar momenta
for the composite non-BPS class of multi-centre black holes. As an application,
we directly solve these equations for the single-centre subclass, and write the
general solution in a manifestly duality covariant form. This includes all
single-centre under-rotating non-BPS solutions, as well as their
non-interacting multi-centre generalisations.Comment: 31 pages, v2: Discussion of the quadratic constraint clarified,
references added, typos corrected, published versio
Fake Superpotential for Large and Small Extremal Black Holes
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. In particular the W function for small non-BPS
black holes can always be computed analytically, unlike for the large
black-hole case.Comment: 30 pages, LaTeX source. Discussion on the radial evolution of the
scalar fields, in relation to the symmetries of the W-function, extended.
Table 1 added. Typos correcte
On the Black-Hole/Qubit Correspondence
The entanglement classification of four qubits is related to the extremal
black holes of the 4-dimensional STU model via a time-like reduction to three
dimensions. This correspondence is generalised to the entanglement
classification of a very special four-way entanglement of eight qubits and the
black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2
supergravity theories.Comment: 32 pages, very minor changes at the start of Sec. 4.1. Version to
appear in The European Physical Journal - Plu
First-order flows and stabilisation equations for non-BPS extremal black holes
We derive a generalised form of flow equations for extremal static and
rotating non-BPS black holes in four-dimensional ungauged N = 2 supergravity
coupled to vector multiplets. For particular charge vectors, we give
stabilisation equations for the scalars, analogous to the BPS case, describing
full known solutions. Based on this, we propose a generic ansatz for the
stabilisation equations, which surprisingly includes ratios of harmonic
functions.Comment: 27 pages; v2: presentation improved and references added as in the
published versio