October 22, 2021

*A positive-definite energy functional for the axisymmetric perturbations of Kerr-Newman black hole spacetimes.*

The mathematical problem of stability of black hole solutions of Einstein’s equations is important to establish the astrophysical significance of these solutions. The problem concerns the stability of the Kerr(-Newman) family of solutions of the Einstein(-Maxwell) equations. In terms of mathematical technique, an important obstacle is that the energy of waves propagating through such spacetimes is not necessarily positive-definite due to the existence of the ergoregion for non-zero angular momentum. In this talk, we shall discuss the proof that there exists an energy functional for axially symmetric linear perturbations of Kerr-Newman that is positive-definite and strictly conserved. The proof is based on a Hamiltonian approach to the Einstein equations and holds for the full sub-extremal range. This is joint work with Vincent Moncrief.