Palette of gravitomagnetic effects

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I shall  analyze three specific general-relativistic  problems in which gravitomagnetism plays important role: the dragging of  magnetic fields  around  rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves (CQG 34, 205006 (2017), Phys. Rev. D 85 124003, (2012) etc). I shall also briefly show how "instantaneous Machian gauges“ can be useful in the cosmological perturbation theory (Phys. Rev. D 76, 063501 (2007)).