Multivalued Entropy of Supersymmetric Black Holes

TL;DR

This paper investigates the entropy of supersymmetric black holes in five-dimensional theories, revealing that entropy depends on the choice of moduli space branch, with multiple solutions sharing identical charges but differing in entropy.

Contribution

It derives supersymmetric flow equations in five-dimensional theories with disjoint moduli space branches and shows how entropy depends on branch choice, introducing new insights into black hole solution multiplicity.

Findings

Black hole entropy depends on the moduli space branch chosen.

Multiple solutions with identical charges can have significantly different entropies.

Entropy is determined by near horizon moduli and branch selection, not just charges.

Abstract

The supersymmetric flow equations describing the flow of moduli from infinity to the black hole horizon, and vice versa, are derived in the five-dimensional theories where the moduli space of the very special geometry has disjoint branches. The multiple solutions are derived from the `off the horizon' attractor equation. Within each branch, the black hole entropy, as usual, depends only on the near horizon attractor values of moduli, i.e. the entropy depends on the charges and on coefficients of the cubic polynomial. It does not depend on the values of the moduli fields at infinity. However, the entropy, as well as the near horizon values of the moduli fields, are shown to depend on the choice of the branch specified by the choice of the set of moduli at infinity. We present examples of BPS black hole solutions with the same Q_I and C_{IJK}, whose entropies differ significantly.