Duality covariant non-BPS first order systems

Abstract

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.

Multi-centered first order formalism

“…We shall generalize the results of [25], matching the treatment given in [12] in the case of the stu model (cfr. section 4.1 therein).…”

“…Note that the vector V λ , which can consistently be defined only in the composite non-BPS class, coincides with the doubly critical vector R introduced in [12], and firstly discussed in the second ref. of [14,15].…”

“…Thus, (5.10) and (5.11) yield 12) which is exactly the expression of the D = 3 rotation pertaining to the BPS multi-centered class [16] subjected to the additional constraint (5.11). The actual meaning of the constraint (5.11) has yet to be clarified; nevertheless, we can here make some observations.…”

“…Multi-centered extremal black hole (BH) solutions in four-dimensional supergravity theories have been widely investigated in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Static BPS black holes in U(1) gauged supergravity

“…It is simple to check using (3.18), combined with (3.16)- Turning the argument around, one can always shift the radial variable so as to arrange that (3.30) leads to 32) holds, which is the choice usually taken in the literature. Alternatively, one may use this freedom to impose c = 0.…”