A new gauge for gravitational perturbations of Kerr spacetimes II: The linear stability of Schwarzschild revisited

Understand

We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations.

• Our approach employs the system of linearised gravity in the new geometric gauge of \cite{benomio_kerr}, specialised to the $|a|=0$ case.
• The proof fundamentally relies on the novel structure of the transport equations in the system.
• Indeed, while exploiting the well-known decoupling of two gauge invariant linearised quantities into spin $\pm 2$ Teukolsky equations, we make enhanced use of the red-shifted transport equations and their stabilising properties to control the gauge dependent part of the system.