Black Holes and Kullback-Leibler Divergence, Decomposing Path-Dependent Processes
Shoshauna Gauvin · Preprints.org · 2025
This work develops an information geometric framework that unifies the principle of stationary action with the minimization of Kullback-Leibler divergence in stochastic systems to probe the shortcomings of General Relativity. By reformulating path probabilities using maximum entropy methods, we decompose complex, path-dependent distributions into symmetric sub-components, thereby isolating error terms that correspond to missing dynamics in black hole mechanics. Analytical and computational analyses reveal that an entropy-maximizing state ΔDKL=0 signifies an ideal match between theory and observation, while deviations expose hidden mechanisms underlying curvature evolution. Extending the approach with Fisher Information Geometry and Ricci flow, we derive a novel relation, γ(T·ds/dE)=dθ/dτ, which links thermodynamic quantities with spacetime expansion dynamics. This connection offers fresh insights into phenomena such as black hole evaporation and event-horizon viscosity. Our findings underscore the necessity of incorporating path-dependence into gravitational models, providing a possible avenue for reconciling classical and quantum descriptions of spacetime evolution.