Black Holes and Flop Transitions in M-Theory on Calabi-Yau Threefolds

TL;DR

We study five-dimensional extreme BPS black holes arising from M-theory compactified on Calabi-Yau threefolds and analyze their behavior across flop transitions in the extended Kähler cone. The analysis leverages the framework of D=5, N=2 supergravity with very special geometry, where the cubic prepotential and real Kähler moduli govern the vector multiplet sector. Focusing on the ${f F}_1$ model, the paper constructs black hole solutions in two chambers II and III connected by a flop, derives stabilization equations, and computes ADM masses and entropies via the central charge. It also demonstrates a concrete interpolating solution between the two vacua, reveals a mild non-smoothness in the space-time at the flop, and identifies conditions for massless black holes at the transition, aligning with M-theory expectations for extra massless states at vanishing cycles.

Abstract

We present fivedimensional extreme black hole solutions of M-theory compactified on Calabi-Yau threefolds and study these solutions in the context of flop transitions in the extended Kahler cone. In particular we consider a specific model and present black hole solutions, breaking half of N=2 supersymmetry, in two regions of the extended Kahler cone, which are connected by a flop transition. The conditions necessary to match both solutions at the flop transition are analysed. Finally we also discuss the conditions to obtain massless black holes at the flop transition.