Thermodynamics and interior structure of density-responsive regular black holes

Abstract This work studies regular black holes motivated by the scalar sector of density-responsive gravity (DRG). An algebraic prescription with phenomenological local running maps a Gaussian matter profile to a diagnostic density profile. A pressure check shows that this profile does not solve the full static DRG equations. It serves only to select an effective metric family with two horizons. The extremal mass is calibrated to M min = √(1 + A /2) M P ≃ 1.006 M P , where A = 0.024 is the historical scalar response amplitude. A fit to ρ ( r ) = ρ 0 exp[-( r / r c ) n ] selects n = 2. The temperature is nonmonotonic, reaching T H max = 0.02547 M P at M = 1.332 M P before vanishing at M min . The calculation verifies the generic scaling near extremality Z tr α ( M − M min ) -1/2 of a static lapse diagnostic for n = 2, 3, 4, 6 and for the Hayward and Bardeen controls. A regulated integral of coordinate time between the horizons provides a static cavity diagnostic, not a prediction of echoes of gravitational waves. The remaining area entropy equals the area entropy already lost at M cross / M 0 = 0.707107 ≃ 1/√2. This geometric crossing does not establish a Page curve or unitarity. The endpoint area entropy is below 2.6% of the initial Bekenstein-Hawking entropy for M 0 = 5 M P and below 0.03% for M 0 = 50 M P . An inverse source reconstruction confirms an isotropic core of de Sitter type but retains the pressure mismatch. An exploratory collapse calculation with an imposed bounce factor produces bounded configurations with 1 - 2 m / r < 0 without establishing formation of the calibrated geometry. The robust results are the calibrated thermodynamics and generic scaling near extremality.