Abstract
Abstract We study extremal black hole solutions to four dimensional $ \mathcal{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.
Highlights
We study extremal black hole solutions to four dimensional N = 2 supergravity based on a cubic symmetric scalar manifold
For theories coupled to a symmetric scalar manifold, as the ones we will deal with, there are three classes of solutions describing interacting ergo-free extremal black holes, distinguished by the algebraic properties of the first order systems that describe them
In this paper we have given a detailed exposition of the first order systems underlying the composite non-BPS system of multi-centre black holes in N = 2 supergravity in four dimensions with a symmetric very special Kahler geometry
Summary
Nv encompass the graviphoton and the gauge fields of the vector multiplets and GμI ν are the dual field strengths, defined in terms of the FμIν though the scalar dependent couplings, whose explicit form will not be relevant in what follows. In this paper we will consider that M4 is a symmetric space, such that the coefficients cijk are left invariant by the action of a group G5 In this case one can define the vielbeins on M4 such that gi ̄ = eiaea ̄,. The scalar fields can equivalently be described by a coset representative υ in G4, and the associated Maurer-Cartan form in the coset component Cnv ∼= g4 ⊖ (u(1) ⊕ k4) is defined as dυυ−1 + υ†−1dυ† = eai dti Ya + eaıdt ̄ı Ya (2.22).
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