Variable MOND Acceleration Scale via Holographic Information Flux: Resolving the Galaxy Cluster Problem

The Modified Newtonian Dynamics (MOND) paradigm successfully explains galaxy rotation curves but fails in galaxy clusters, requiring ~10× higher acceleration scales. We propose a resolution based on Verlinde's emergent gravity framework extended with a variable acceleration threshold determined by local supermassive black hole (SMBH) density. The key mechanism is an information flux through black hole horizons scaling with horizon area (Φ ∝ M²), following from the holographic principle. We derive, without free parameters, that the enhancement scales as a₀ ∝ N^0. 4, matching CLASH survey data within 6%. We also present observational evidence from Abell 520 showing a 1. 53× overdensity of compact sources in the "dark core, " consistent with stripped SMBH hosts predicted by the framework.