Bekenstein--Hod Bound: A $3.3σ$ Confirmation from GW250114

Abstract

Black holes link gravity, thermodynamics and information via limits on the relaxation rate of a perturbed system. The Bekenstein-Hod bound imposes a minimum relaxation time at fixed temperature, but its observational test demands both black hole thermodynamic characterization and decay time measurement. Here we test this bound with GW250114, the loudest gravitational-wave signal yet observed from a binary black-hole merger. We infer the remnant temperature from pre-merger data truncated at least $10\,M$ before the peak and its longest-lived decay time from post-merger data, thereby avoiding direct reuse of the same strain samples. The ringdown frequencies and damping times are allowed to vary independently rather than being fixed to the Kerr spectrum. For the primary $t_{<}=-10\,M$ analysis, the bound is verified at $3.3-3.6σ$ across the focal ringdown start times, representing a substantial improvement over the $91\%$ confidence level set by GW150914. The conclusion remains robust under varied pre-merger cutoffs and explicit inclusion of the short-lived first overtone in waveform modelling. This separated-data measurement converts an information-theoretic relaxation bound into a precision test of a single astrophysical black hole.