Self-contained expositions written in a course-style format
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ADM_formalism.pdfADM Formalism
ADM Formalism
These notes present a rigorous, geometric formulation of the ADM (3+1) decomposition of General Relativity. Starting from a spacetime foliation by Cauchy hypersurfaces, the construction develops the induced geometry, projection operators, intrinsic covariant derivative, and the Gauss–Codazzi–Ricci equations in a systematic and self-contained way. This framework is then used to derive the Hamiltonian formulation of gravity, including the constraint equations and their algebra.
Information Geometry
Information Geometry
These notes introduce information geometry starting from a divergence function as the primary object. Under suitable regularity assumptions, the metric, dual affine connections, and induced geometric structures of a statistical manifold are obtained directly from the divergence. This viewpoint unifies and generalizes standard constructions such as the Fisher information metric and alpha-connections.
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