Understand
We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e.
- solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield with closed orbits.
- While building on the remarkable advances made in last 15 years on establishing quantitative linear stability, the paper introduces a series of new ideas among which we emphasize the general covariant modulation (GCM) procedure which allows us to construct, dynamically, the center of mass frame of the final state.
- The mass of the final state itself is tracked using the well known Hawking mass relative to a well adapted foliation itself connected to the center of mass frame.