In this paper, we study spherical gravitational collapse of inhomogeneous
pressureless matter in a well-defined $n \rightarrow4$d limit of the
Einstein-Gauss-Bonnet gravity. The collapse leads to either a black hole or a
massive naked singularity depending on time of formation of trapped surfaces.
More precisely, horizon formation and its time development is controlled by
relative strengths of the Gauss-Bonnet coupling $(\lambda)$ and the
Misner-Sharp mass function $F(r,t)$ of collapsing sphere. We find that, if
there is no trapped surfaces on the initial Cauchy hypersurface and $F(r,t)<
2\sqrt{\lambda}$, the central singularity is massive and naked. When this
inequality is equalised or reversed, the central singularity is always censored
by spacelike/timelike spherical marginally trapped surface of topology
$S^{2}\times \mathbb{R}$, which eventually becomes null and coincides with the
event horizon at equilibrium. These conclusions are verified for a wide class
of mass profiles admitting different initial velocity conditions. Hence, our
result implies that the $4$d Einstein-Gauss-Bonnet generically violates the
cosmic censorship conjuncture. Further implications of this violation from the
perspective of visibility of causal signals from the spacetime singularity are
also discussed.
