Part VIII: Lagrangian Connections

From the Einstein–Hilbert action to Bondi news — a unified variational framework connecting Perelman's Ricci flow, the spin memory effect, and general relativity through their Lagrangian structures.

This module develops the deep Lagrangian connections between six apparently disparate frameworks: the Einstein–Hilbert action, the GHY boundary term, the ADM Hamiltonian, Perelman's $\mathcal{F}$-functional, the Bondi–Sachs action at null infinity, and the Mabuchi K-energy on the celestial sphere. All are shown to be facets of a single variational structure whose gradient flows, Noether charges, and BRST cohomology encode the complete physics of gravitational memory.