Split Attractor Flow in N=2 Minimally Coupled Supergravity

TL;DR

This paper classifies the stability and split attractor flows of two-center extremal black holes in N=2 supergravity, revealing the structure of walls and the behavior of BPS and non-BPS solutions with implications for black hole entropy and stability.

Contribution

It provides a detailed classification of stability regions, walls, and flow dynamics for two-center black holes in minimally coupled N=2 supergravity, including non-BPS cases.

Findings

Two-center charge orbits support stability or anti-marginal stability walls, but not both.

The BPS mass of the composite never vanishes within the scalar manifold.

Entropy inequalities prevent entropy enigma decays in these models.

Abstract

We classify the stability region, marginal stability walls (MS) and split attractor flows for two-center extremal black holes in four-dimensional N=2 supergravity minimally coupled to n vector multiplets. It is found that two-center (continuous) charge orbits, classified by four duality invariants, either support a stability region ending on a MS wall or on an anti-marginal stability (AMS) wall, but not both. Therefore, the scalar manifold never contains both walls. Moreover, the BPS mass of the black hole composite (in its stability region) never vanishes in the scalar manifold. For these reasons, the "bound state transformation walls" phenomenon does not necessarily occur in these theories. The entropy of the flow trees also satisfies an inequality which forbids "entropy enigma" decays in these models. Finally, the non-BPS case, due to the existence of a "fake" superpotential satisfying a triangle inequality, can be treated as well, and it can be shown to exhibit a split attractor flow dynamics which, at least in the n=1 case, is analogous to the BPS one.