A Difference Between Event Horizons & Trapped Surfaces - Explained Simply

[Nick Prince]

Can anyone please explain to me in simple terms what the difference is between a trapped surface and an event horizon. I'm not familiar with global general relativity so cannot understand any of the results I've looked up by googling. I think that Tipler has said that when the future C-boundary of a collapsing universe is a single point then there will be no event horizons. moreover, event horizons can totally vanish if the universe is spatially compact which is to say it is closed. I really need an intuitive idea of the difference between an event horizon and a trapped surface.

Any help gratefully received.

 

[PeterDonis]

Can anyone please explain to me in simple terms what the difference is between a trapped surface and an event horizon.

A trapped surface is a surface at which, locally, radially outgoing light does not increase its radial coordinate, but stays at the same one.

An event horizon is a surface at which, globally, radially outgoing light emitted at that surface will never reach infinity.

The difference is in the words I highlighted above. One is a local concept, the other is a global concept.

An example of the difference would be a black hole that is about to accrete some matter. Suppose you are hovering just above the hole's horizon before the matter falls in. You measure local radially outgoing light and find that it does move outward (increase its radial coordinate). That means you are above the trapped surface, and therefore might feel safe.

However, unbeknownst to you, a short time later, the matter falls past you and into the hole, and suddenly your measurements of radially outgoing light change--now the light is no longer moving outward! You are trapped! How did this happen?

What happened was that, unbeknownst to you, you were already inside the event horizon, even though you were outside the trapped surface. The event horizon is determined globally--what happens to light not just locally, right now, but all the way into the future. That radially outgoing light that you measured before the matter fell in, and found it moving outward, was actually going to stop moving outward in the future, when the matter fell in, because that matter increased the mass of the hole, and the increased mass increased the hole's gravity and stopped that light from moving outward any further.

 

[Nick Prince]

Ok thank you for that. What about Tipler's claim then. Does it make sense?

Can an event horizon be thought of as a weak form of a trapped surface which disappears if the universe ends in a c-boundary which is a single point?

 

[PeterDonis]

Can an event horizon be thought of as a weak form of a trapped surface which disappears if the universe ends in a c-boundary which is a single point?

No. In Tipler's "Omega Point" universe there are no event horizons at all. There might be trapped surfaces, but they are only temporary; the things trapped inside them don't stay trapped.

Note that Tipler does not, as far as I know, actually write down his solution explicitly; he just defines it by the property that the "Omega Point" at the end has as its past light cone the entire universe. That rules out the possibility of event horizons, since any regions of spacetime behind event horizons would by definition not be in the past light cone of the rest of the universe, including the Omega Point.

 

[Nick Prince]

Is this a realistic possibility then I'm still confused. How do trapped surfaces differ from event horizons? Is there some intuitive way of defining the two?

 

[Nick Prince]

I know you have given a definition but can you elaborate regarding trapped surfaces?

 

[PeterDonis]

Is this realistic then.

Is what realistic? Tipler's model? I have no idea. It's a speculation on his part which AFAIK has gotten no traction in the GR community. As I said, I don't think he's written the solution down explicitly, so there's no way to check if it's actually possible or not.

How do trapped surfaces differ from event horizons? Is there some intuitive way of defining the two?

I already did in ordinary language, but since you marked this thread as "A" level I'll give the more technical definitions.

A trapped surface (more precisely a "Marginal Outer Trapped Surface", which is the thing you're interested in--there are other kinds of trapped surfaces that aren't relevant here) is a surface on which the expansion of the congruence of outgoing null normals is zero.

An event horizon is the boundary of a region of spacetime (a "black hole") which is not in the causal past of future null infinity.

 

[PeterDonis]

can you elaborate regarding trapped surfaces?

What do you want me to elaborate?

 

[Nick Prince]

Thank you for that PeterDonis That helps a lot.
Kindest regards