Can Zeeman effect occurs in gravitational wave from binary blackhole-magnetar merger I understand that Zeeman effect is behind the splitting of spectrum lines in an atom in strong magnetic field, I was wondering if such phenomenon could occur outside electromagnetic wave such as from the frequencies of gravitational wave emitted by powerful events such as inspiral between blackhole and neutron star with extremely powerful magnetic field?
 A: It is unclear what the OP exactly would consider an analog of the Zeeman effect on BH-magnetar merger. Such a merger is not characterized by discrete frequencies that could be shifted or split. However, at least in principle, the waveform of such a merger should carry the imprint of the magnetars magnetic field. (E.g. the orbital motion of the magnetar, implies a changing magnetic field leading to addition energy loss in EM radiation, thereby accelerating the merger.)
The closest analog of the atomic spectrum in gravitational physics is the quasinormal mode (QNM) spectrum of a black hole. This the spectrum of characteristic frequencies (and decay rates) with which a black hole settles down to its equilibrium state (e.g. after a merger). For example, the "ringdown" seen at the end of a binary merger is a superposition of QNMs. This spectrum discrete in analogy to the spectrum of an atom, and is determined by the properties of the black hole (mass, angular momentum, charge).
It has been shown that this QNM spectrum is in fact modified when an external magnetic field is applied to the black hole (see https://arxiv.org/abs/0707.1156, they only show that this is the case for scalar QNMs, but it should hold for gravitational QNMs just as well.) Moreover, in analogy with the Zeeman effect, this shifting actually breaks the degeneracy between the different "m-modes" of the spectrum.
