DOI: 10.1140/epjc/s10052-026-16149-2 ISSN: 1434-6052
Interior geometry of black holes as a probe of first-order phase transition
Zi-Qiang Zhao, Zhang-Yu Nie, Shao-Wen Wei, Jing-Fei Zhang, Xin Zhang Abstract
Traditional diagnostics of black hole phase transitions rely on thermodynamic quantities defined at the event horizon or asymptotic boundary. Here, we demonstrate that the near-singularity geometry offers a sharp, independent probe of both first-order phase transitions and supercritical crossover. For scalarized AdS black holes exhibiting a first-order phase transition, the Kasner exponent
$$p_t$$
p
t
, which characterizes the approach to the singularity, undergoes a dramatic transformation. On one side of the transition,
$$p_t$$
p
t
oscillates strongly with temperature, reflecting violent interior dynamics. On the other side, it becomes a smooth, monotonically varying function. These two distinct behaviors converge as the critical point is approached. Beyond the critical point, in the supercritical region,
$$p_t(T)$$
p
t
(
T
)
develops a distinct extremum, defining a “Kasner crossover line” that is entirely independent of traditional thermodynamic (Widom line) or dynamic (Frenkel line) criteria. Our work establishes the near-singularity geometry of scalarized black holes as a novel class of diagnostics for phase transitions, revealing that a change in the macroscopic thermodynamic state fundamentally reshapes the deepest interior structure of spacetime.