Shuo Xiao, Shuang-Nan Zhang

A nearby primordial-black-hole (PBH) evaporation burst would produce a curved gamma-ray wavefront, leading to detectable departures from plane-wave inter-satellite delays. We introduce a purely geometric method that combines imaging localizations with multi-spacecraft timing to determine the distance of a gamma-ray transient. Applied to \textit{Swift}-localized short GRBs, the current sample shows no significant deviation from the plane-wave expectation, with the most constraining event reaching $1.2$ AU and already probing a meaningful Solar-System-scale regime. Our analysis shows that direct distance measurements are achievable to $10^3$ AU scales with the current and near-future technical capabilities. Once a finite source distance is measured, the corresponding PBH mass and lifetime can be directly inferred. Future wide-field localization and long-baseline deep-space gamma-ray detectors could extend such searches to $10^5$ AU and beyond.