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 all strong–gravity and information tests present in the documentation: neutron–star and Super–TOV configurations that fix the high–density scalar stiffness; tests of intermediate–mass and microscopic black holes; a “Sad Trombone” fast–radio–burst test which constrains scalar relaxation and feeds into microscopic evaporation; ringdown tests (including scalar breathing modes and quasinormal–mode deviations), shadow and photon–ring tests, and modified ISCO spectra that reveal spin–scalar–charge degeneracies. Dedicated information–paradox tests quantify the deviation of MMA–DMF quasinormal modes from Kerr, the structure of gravitational–wave echoes, and the Total Determinism Test for Black Holes (TDT–BH), which relates the corrected entropy, echo delays and quasinormal–mode shifts across the full mass spectrum from microscopic remnants to supermassive objects. 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 a combination of regular cores, long–lived remnants and delayed echo channels. At the same time, the model predicts specific observational signatures—in particular, millisecond–scale echoes in stellar–mass mergers, percent–level deviations in higher–order quasinormal modes and degeneracies between spin and scalar charge in accretion spectra—which render its proposed resolution of the information and entropy paradoxes empirically falsifiable.