Complex spinodals and supercritical crossovers in Kerr–Newman–AdS4

Determine whether the analytic continuation of complex spinodals in Kerr–Newman–AdS4 organizes the supercritical crossover and its Widom-line structure, thereby connecting complex black-hole saddles with real thermodynamic response.

Background

The paper distinguishes local saddle degeneracies, thermodynamic phase coexistence, and contour-selected zeros of the partition function. In its fixed-angular-momentum extended-thermodynamics analysis, real spinodal branches terminate at a critical point, while their analytic continuations persist in complex thermodynamic parameter space and may be related to projected Widom-type lines.

The authors identify Kerr–Newman–AdS4 as a natural setting for testing whether complex spinodal branches encode information about supercritical crossover behavior and real response functions. This question is left for forthcoming work rather than resolved in the present Kerr–AdS5 analysis.

References

A natural extension of this work is the study of complex spinodals and supercritical crossovers in Kerr--Newman--AdS$_4$ black holes. Although the real spinodal branches terminate at criticality, their analytic continuation into complex thermodynamic parameter space may retain information about the underlying saddle structure. In forthcoming work, we will investigate whether these complex spinodals organize the supercritical crossover and its Widom-line structure, providing a direct connection between complex black hole saddles and real thermodynamic response.

— Complex Phase Structure of Kerr-AdS$_5$ Black Holes: Critical Saddles and Fisher Zeros  (2609.39085 - Lee et al., 30 Sep 2026) in Section 8, paragraph beginning “A natural extension of this work”