non-BPS walls of marginal stability

TL;DR

This paper investigates non-BPS multi-centre extremal black holes in N=2 supergravity, demonstrating positive binding energy and the existence of walls of marginal stability, with solutions constrained to specific hypersurfaces in moduli space.

Contribution

It provides an explicit description of non-BPS multi-centre solutions and proves the existence of walls of marginal stability in the moduli space.

Findings

Binding energy of composite solutions is always positive.

Walls of marginal stability exist for generic charge configurations.

Two-centre solutions are confined to a specific hypersurface in moduli space.

Abstract

We explore the properties of non-BPS multi-centre extremal black holes in ungauged N=2 supergravity coupled to n_v vector multiplets, as described by solutions to the composite non-BPS linear system. After setting up an explicit description that allows for arbitrary non-BPS charges to be realised at each centre, we study the structure of the resulting solutions. Using these results, we prove that the binding energy of the composite is always positive and we show explicitly the existence of walls of marginal stability for generic choices of charges. The two-centre solutions only exist on a hypersurface of dimension n_v+1 in moduli space, with an n_v-dimensional boundary, where the distance between the centres diverges and the binding energy vanishes.