Considering the evolution of a perfect fluid with self-similarity of the second kind, we find that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along timelike geodesics with a self-similar parameter α = -3. Since the metric obtained is not asymptotically flat, we match the space–time of the fluid with a Schwarzschild space–time. All the energy conditions are fulfilled until the naked singularity.
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