A recent study has investigated the gravitational collapse of dust within the framework of Lovelock gravity, an extension of general relativity that includes higher-order curvature terms. The findings suggest that these higher-order Lovelock terms do not restore local cosmic censorship but instead promote the local visibility of central shell-focusing singularities. This implies that, under certain conditions, the singularities resulting from collapse could be observable from the outside, contravening the cosmic censorship hypothesis which postulates that singularities must be hidden by event horizons.

The analysis focused on the collapse branch with a positive highest-order Lovelock coefficient, \(c_N\). It was found that the highest nonvanishing Lovelock order, \(N\), controls both the near-singularity collapse and the formation of trapped surfaces. In noncritical dimensions (where \(D-1-2N>0\)), the apparent-horizon curve approaches the singularity curve with a trapping exponent \(β_N=(D-1)/(D-1-2N)\). The condition for local singularity visibility is established by comparing this exponent with the first nonvanishing correction \(r^\ell\) to the singularity curve, resulting in \(\ell<β_N\), provided the singularity curve opens outward. This means that increasing \(N\) enlarges the class of inhomogeneous initial data producing outgoing radial null rays from the central singularity.

In the critical odd-dimensional branch, where \(D=2N+1\), no apparent horizon forms sufficiently close to the center. In this case, any outward opening of the singularity curve leads to local visibility. The locally visible singularities are Królak-strong along the emerging null rays, reaching Tipler strength at the threshold. For bound and unbound collapse, the noncritical exponents remain unchanged; the energy function modifies the opening of the singularity curve, while in the critical branch, it enters the leading terminal collapse velocity. These findings are crucial for understanding singularity formation in theories of gravity beyond general relativity and their implications for cosmic censorship.