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.