Year: 2026
Type: preprint
Abstract: We establish a saddle-order proposition for the ensemble-averaged generalized free energy in reduced Euclidean black hole ensembles. Under regularity and stability assumptions, the leading fluctuation contribution is determined by the order of the first stabilizing term around the dominant saddle. An ordinary critical point is governed by a quartic soft mode, giving a quarter-temperature contribution instead of the familiar half-temperature Gaussian result. We verify this analytically for four-dimensional RN-AdS and Kerr-AdS black holes and map their thermodynamic controls to a common quartic normal form, whose scaling function connects the critical and Gaussian regimes along the zero-field one-well direction. The proposition also extends to coupled collective modes with weighted-homogeneous leading potentials. These results provide a unified description of reduced-ensemble fluctuations through black hole criticality.
Source: arXiv (Cornell University)
Authors: Anand, Ankit, Cheng, Peng
Institution: Indian Institute of Technology Kanpur
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4317857312, G72192826
OpenAlex ID: W7214047320