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Abstract We propose that chirally asymmetric plasma can be produced in the gap regions of the magnetospheres of pulsars and black holes. We show that, in the case of supermassive black holes situated in active galactic nuclei, the chiral charge density and the chiral chemical potential are very small and unlikely to have any observable effects. In contrast, the chiral asymmetry produced in the magnetospheres of magnetars can be substantial. It can trigger the chiral plasma instability that, in turn, can lead to observable phenomena in magnetars. In particular, the instability should trigger circularly polarized electromagnetic radiation in a wide window of frequencies, spanning from radio to near-infrared. As such, the produced chiral charge has the potential to affect some features of fast radio bursts. 

About eight years ago it was predicted theoretically that a charged chiral plasma could support the propagation of the so-called chiral magnetic waves, which are driven by the anomalous chiral magnetic and chiral separation effects. This prompted intensive experimental efforts in search of signatures of such waves in relativistic heavy-ion collisions. In fact, several experiments have already reported a tentative detection of the predicted signal, albeit with a significant background contribution. Here, we critically reanalyze the theoretical foundations for the existence of the chiral magnetic waves. We find that the commonly used background-field approximation is not sufficient for treating the waves in hot chiral plasmas in the long-wavelength limit. Indeed, the back-reaction from dynamically induced electromagnetic fields turns the chiral magnetic wave into a diffusive mode. While the situation is slightly better in the strongly-coupled near-critical regime of quark-gluon plasma created in heavy-ion collisions, the chiral magnetic wave is still strongly overdamped due to the effects of electrical conductivity and charge diffusion.