  Accreting binary black holes (BBHs) are multi-messenger sources, emitting
copious electromagnetic (EM) and gravitational waves. One of their most
promising EM signatures is the lightcurve modulation caused by a strong, unique
and extended azimuthal overdensity structure orbiting at the inner edge of the
circumbinary disc (CBD), dubbed "lump". In this paper, we investigate the
origin of this structure using 2D general-relativistic (GR) hydrodynamical
simulations of a CBD in an approximate BBH spacetime. First, we use the
symmetric mass-ratio case to study the transition from the natural m = 2 mode
to m = 1. The asymmetry with respect to m = 2 grows exponentially, pointing to
an instability origin. We indeed find that the CBD edge is prone to a
(magneto-)hydrodynamical instability owing to the disc edge density sharpness:
the Rossby Wave Instability (RWI). The RWI criterion is naturally fullfilled at
the CBD edge and we report the presence of vortices, which are typical
structures of the RWI. The RWI is also at work in the asymmetric mass-ratio
cases (from 0.1 to 0.5). However, the CBD edge sharpness decreases with a
decreasing mass ratio, and so the lump. By proposing a scenario for this lump
formation, our work further supports its existence in astrophysical CBDs and
potential source for an EM signature of BBHs. Finally, because the RWI is not
caused by GR effects, it is also a robust candidate for the lump origin in CBDs
around non-compact objects, e.g. binary protostars.
