Warp propagation in astrophysical discs

Astrophysical discs are often warped, that is, their orbital planes change with radius. This occurs whenever there is a non-axisymmetric force acting on the disc, for example the Lense–Thirring precession induced by a misaligned spinning black hole, or the gravitational pull of a misaligned companion. Such misalignments appear to be generic in astrophysics. The wide range of systems that can harbour warped discs—protostars, X-ray binaries, tidal disruption events, quasars and others—allows for a rich variety in the disc’s response. Here we review the basic physics of warped discs and its implications.