Evolutionary algorithms for multi-center solutions

TL;DR

This paper introduces an optimization method combining evolutionary algorithms and Bayesian optimization to systematically construct multi-center supergravity solutions that meet physical constraints, enabling the discovery of complex black hole microstate configurations.

Contribution

It presents a novel computational approach for generating multi-center supergravity solutions with multiple centers and physical parameter ranges.

Findings

Explicit five-center solutions constructed.

Explicit seven-center solutions constructed.

Solutions satisfy all physical constraints.

Abstract

Large classes of multi-center supergravity solutions have been constructed in the study of supersymmetric black holes and their microstates. Many smooth multi-center solutions have the same charges as supersymmetric black holes, with all centers deep inside a long black-hole-like throat. These configurations are constrained by regularity, absence of closed timelike curves, and charge quantization. Due to these constraints, constructing explicit solutions with several centers in generic arrangements, and with all parameters in physically relevant ranges, is a hard task. In this work we present an optimization algorithm, based on evolutionary algorithms and Bayesian optimization, that systematically constructs numerical solutions satisfying all constraints. We exhibit explicit examples of novel five-center and seven-center machine-precision solutions.