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.
