Black Holes in the MMA–DMF Framework: Resolving the Information and Entropy Paradoxes

The MMA–DMF framework modifies gravity by adding a single geometric scalar degree of freedom with a characteristic energy scale of order 100 TeV. In this work we assemble the black–hole sector of MMA–DMF and show how it leads to a concrete, testable resolution of both the entropy and information paradoxes. Starting from a static, spherically symmetric regular metric with a de Sitter core, we derive the thermodynamic quantities of MMA–DMF black holes, including a corrected entropy SMMA–DMF(A), a modified evaporation law with a finite remnant mass, and a self–consistent Page curve in which the black–hole entropy decreases while the radiation entropy increases, saturates and eventually falls. We then systematise strong–gravity and information tests: neutron–star and Super–TOV configurations; intermediate–mass and microscopic black holes; a “Sad Trombone” fast–radio–burst test; ringdown tests (including scalar breathing modes and quasinormal–mode deviations), shadow and photon–ring tests, and modified ISCO spectra. Dedicated information–paradox tests quantify deviations from Kerr, gravitational–wave echoes, and the Total Determinism Test for Black Holes (TDT–BH), relating corrected entropy, echo delays and quasinormal–mode shifts across the full mass spectrum. Using these ingredients we demonstrate that MMA–DMF black holes are free of curvature singularities, possess a finite and computable entropy at all stages of their evolution, obey a generalised second law and can preserve quantum information through regular cores, long–lived remnants and delayed echo channels, while predicting falsifiable observational signatures