Higher Lovelock Curvature Terms Favor Local Nakedness in Dust Collapse

We show that higher-curvature Lovelock terms do not restore local cosmic censorship in spherical dust collapse, but instead promote the local visibility of central shell-focusing singularities. On the collapse branch with positive highest-order Lovelock coefficient $c_N$, the highest nonvanishing Lovelock order $N$ controls both the near-singularity collapse and the formation of trapped surfaces. In noncritical dimensions, $D-1-2N>0$, the apparent-horizon curve approaches the singularity curve with trapping exponent ${\beta }_N=(D-1)\mathrm{/}(D-1-2N)$. Comparing this scale with the first nonvanishing correction $r^{\mathrm{\ell }}$ to the singularity curve gives the local-visibility condition $\mathrm{\ell }<{\beta }_N$, provided the singularity curve opens outward. Thus increasing $N$ enlarges the class of inhomogeneous initial data producing outgoing radial null rays from the central singularity. In the critical odd-dimensional branch, $D=2N+1$, no apparent horizon forms sufficiently close to the center, so any outward opening of the singularity curve gives local visibility. The locally visible singularities are Królak-strong along the emerging null rays, with Tipler strength reached at threshold. For bound and unbound collapse, the noncritical exponents are unchanged: the energy function modifies the opening of the singularity curve, while in the critical branch it enters the leading terminal collapse velocity.