Schottky Anomaly and Microstructure of de Sitter Black Holes in Conformal Killing Gravity

Abstract

We investigate the thermodynamic properties of charged de Sitter (dS) black holes in Conformal Killing Gravity (CKG), whose static spherically symmetric metric contains the quartic term [Formula: see text]. By treating the spacetime region between the event and cosmological horizons as a single effective thermodynamic system, we obtain closed-form expressions for the effective temperature, entropy, pressure, and electric potential of an exact charged de Sitter solution of conformal Killing gravity, and show that these quantities satisfy a generalized first law together with a Smarr relation in which the conformal coupling acquires its own conjugate potential. The heat capacity exhibits Schottky-type maxima in both the canonical and grand canonical ensembles, with the peak horizon ratio essentially independent of the coupling ([Formula: see text]) while the peak temperature rises from 0.240 to 0.349 and the peak amplitude falls from 0.114 to 0.054 as [Formula: see text] increases from 1.6 to 12. The corresponding effective number of thermodynamic degrees of freedom decreases from [Formula: see text] to [Formula: see text]. We interpret this as a phenomenological two-level thermodynamic analogy rather than evidence for a discrete quantum spectrum. We also explore the effect of the conformal coupling constant [Formula: see text] and the de Sitter curvature scale on thermodynamic stability and effective degrees of freedom.