In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in $n$ dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat depending on the choice of the cosmological constant. Using the asymptotically flat solution for $n\ge 7$ with a power-law form of the mass as a function of the null coordinate, we present a model for a gravitational collapse in which a null dust fluid radially injects into an initially flat and empty region. It is found that a naked singularity is inevitably formed whose strength is different for the $n=7$ and $n\ge 8$ cases. In the $n=7$ case, the limiting focusing condition for the strength of curvature singularity is satisfied. But for $n\ge 8$, the strength of curvature singularity depends on the rate of increase of mass of the spacetime. These considerations show that the third order Lovelock term weakens the strength of the curvature singularity.

• Received 12 June 2008

DOI:https://doi.org/10.1103/PhysRevD.78.064015