Are Trapped Surfaces Visible?

In 1965, Penrose introduced the idea of a trapped surface which became an essential concept in proving the first singularity theorem. In this work, some neglected aspects of trapped surfaces are considered. Specifically, I discuss that the existence of such a surface in space-time may result in an undesirable consequence: either space-time is singular, or chronology violation arises. Although a trapping region often implies a singularity in space-time, but a singular space-time may not contain any trapped region. Finally, I show that noncosmological trapped surfaces are observer-dependent. It means that some observers in a trapped region may not observe trapped surfaces!