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We obtain a general spherically symmetric solution of a null dust fluid in $n(\geq 4)$-dimensions in Gauss-Bonnet gravity. This solution is a generalizationof the $n$-dimensional Vaidya-(anti)de Sitter solution in general relativity.For $n=4$, the Gauss-Bonnet term in the action does not contribute to the fieldequations, so that the solution coincides with the Vaidya-(anti)de Sittersolution. Using the solution for $n \ge 5$ with a specific form of the massfunction, we present a model for a gravitational collapse in which a null dustfluid radially injects into an initially flat and empty region. It is foundthat a naked singularity is inevitably formed and its properties are quitedifferent between $n=5$ and $n \ge 6$. In the $n \ge 6$ case, a masslessingoing null naked singularity is formed, while in the $n=5$ case, a massivetimelike naked singularity is formed, which does not appear in the generalrelativistic case. The strength of the naked singularities is weaker than thatin the general relativistic case. These naked singularities can be globallynaked when the null dust fluid is turned off after a finite time and the fieldsettles into the empty asymptotically flat spacetime.Comment: 10 pages, 2 figures, final version to appear in Classical and Quantum  Gravit

Effects of Gauss–Bonnet term on the final fate of gravitational collapse