Exact Attractive Non-BPS STU Black Holes
Renata Kallosh, Navin Sivanandam, Masoud Soroush
TL;DR
The paper establishes that non-BPS STU black holes admit exact, globally defined solutions obtained by replacing charges with harmonic functions in horizon expressions, yielding explicit moduli and a metric determined by the symplectic invariant $I_1$. It demonstrates a concrete non-BPS D2-D6 attractor and, via $[SL(2,oldsymbol{Z})]^3$ duality, extends this to generic charge configurations; it also argues for the existence of stationary, multi-centered non-BPS attractors and conjectures that such configurations can resolve apparent single-center instabilities. The work highlights the attractor mechanism beyond supersymmetry, leverages U-duality to generate broad classes of solutions, and suggests a split attractor-flow picture for non-BPS black holes with potential implications for stability and microstate structure. Overall, the results provide a robust framework for exact non-BPS STU black-hole solutions and pave the way for further exploration of multi-center non-BPS configurations in extremal gravity theories.
Abstract
We develop some properties of the non-BPS attractive STU black hole. Our principle result is the construction of exact solutions for the moduli, the metric and the vectors in terms of appropriate harmonic functions. In addition, we find a spherically-symmetric attractor carrying $p^0$ ($D6$ brane) and $q_a$ ($D2$ brane) charges by solving the non-BPS attractor equation (which we present in a particularly compact form) and by minimizing an effective black hole potential. Finally, we make an argument for the existence of multi-center attractors and conjecture that if such solutions exist they may provide a resolution to the existence of apparently unstable non-BPS ``attractors.''