Closed trapped surfaces in higher dimensional self-similar Vaidya spacetime

Masahiro Shimano and Tomohiro Harada

We discuss closed trapped surfaces and a naked singularity in higher dimensional Vaidya spacetime with a self-similar mass function. By using two kinds of $D-2$ surfaces, we construct closed trapped surfaces which begin in a flat region, pass through a higher dimensional self-similar Vaidya region, and end in a higher dimensional Schwarzschild region. Hence, closed trapped surfaces extend into a flat region. Moreover, we demonstrate that the naked singularity is absence, if spacetime has closed trapped surfaces as above.