I have a question on horizons. Actually I would like to make some things that I have in mind clear. First of all let's give some definitions. Trapped surface: Is a surface on which null vectors point inwards. That means that for example, if we let a photon on that surface it could only travel inwards and it could at no time be outside that surface. Untrapped surface: Is a surface on which there exist null vectors pointing outwards. That means that for example, if we let a photon on that surface, there are null geodesics leading out of that surface. Marginally trapped surface: Is a surface on which there exist null vectors that are tangent to that surface but there are no null vectors pointing outwards. A first question could be how exact are those definitions. The question I would actually like to ask is: What exactly is the difference between an event horizon and an apparent horizon in terms of trapped surfaces and null geodesics? As I understand the subject, an apparent horizon is defined as a trapped surface that is the border between a region that has outgoing null geodesics that point outwards and a region that doesn't have outgoing null geodesics pointing outwards. That means that the apparent horizon is the lust trapped surface between the two regions and the next infinitesimally near surface is an untrapped surface. On the other hand an event horizon is a marginally trapped surface an thus it is also a null surface, in the sense that it has null generators, and it is an asymptotic surface to the outgoing null geodesics from the inside and the outside. These things can be seen in the following diagram of the formation of a spherically symmetric black hole, were the cyan lines are the null ingoing geodesics, the yellow lines are the null outgoing geodesics, the green line is the apparent horizon and the event horizon is defined by the convergence of the yellow lines. We can see that at late times the two horizons coincide. In the above example, it is easy to identify the horizons and distinguish between the event horizon and the apparent horizon. Both horizons are trapped surfaces as it can be seen by the light cones, but the event horizon is also a null surface while the apparent horizon isn't at early times. Will these criteria apply to more general configurations or should I look for a more general "tool"? The point is, are these things generic? The case in the diagram is a special case with a lot of symmetry. Are the above definitions general or they apply only to especially symmetric settings like the above? What are the other trademarks that distinguish these horizons? Vagelford PS. The x-axis is distance r and the y-axis is time t.