The MOTS-stability spectral problem: when `non-normal' is generic

30.06. bis 30.06.2022, 14:00-16:00  –  C6H05 Tübingen, 2.09.2.22 Campus Golm
Geometric Analysis, Differential Geometry and Relativity

José Luis Jaramillo

The spectral theorem provides a powerful tool to study physical systems 
controlled by a self-adjoint or, more generally, normal operator. The situation changes  qualitatively when the normal character of the operator is lost. Issues such as spectral  instability or the assessment of the spectral expansions in terms of eigenfunctions become more  delicate. Here we discuss a non-normal spectral problem occurring in a black hole setting.  Specifically, it concerns the
MOTS-stability operator controlling the dynamics of apparent horizon  world-tubes, a non-selfadjoint operator for rotating black holes. Specifically, it is shown that such  an operator is non-normal whenever the rotation (Hajicek) form is not Killing, which is indeed the  generic situation. The natural question to assess is if the potential MOTS-spectral instability  is actually present and, if so, its possible implications for binary black hole mergers. As a  warming-up exercise, we
explore numerically the MOTS-spectral problem in two simple but  significant and complementary cases, namely: the Kerr black hole (non-normal) case, on the one hand, 
and the head-on binary black hole collision (normal) case, on the other hand.