A new gauge for gravitational perturbations of Kerr spacetimes I: The linearised theory

Understand

We propose a new geometric framework to address the stability of the Kerr solution to gravitational perturbations in the full sub-extremal range $|a|<M$.

• Central to our framework is a new formulation of nonlinear gravitational perturbations of Kerr, whose two novel ingredients are the choice of a geometric gauge and non-integrable null frames both tailored to the outgoing principal null geodesics of Kerr.
• The vacuum Einstein equations for the perturbations are formulated in our gauge as a system of equations for the connection coefficients and curvature components relative to the chosen frames.
• When renormalised with respect to Kerr, the null structure equations with the form of outgoing transport equations do not possess any derivatives of renormalised connection coefficients on the right hand side.