# Light cone = black hole?

1. Jan 4, 2010

### Hurkyl

Staff Emeritus
A forward light-cone is a surface that defines a region from which light cannot escape.

Similarly, a backward light-cone defines a region that light cannot enter.

What distinguishes these from event horizons?

2. Jan 4, 2010

### diazona

As far as I know, not much except for the fact that a black hole has a singularity. In fact, you can draw a representation of spacetime around a black hole so that the event horizon looks just like a light cone. There's a nice picture here:
http://en.wikipedia.org/wiki/Penrose_diagram
(second picture down, the Schwarzschild solution, is what I had in mind)

3. Jan 5, 2010

### atyy

Something about future null infinity. From Wald, the crucial distinction between the event horizon and the future light cone of a point in Minkowski space is that the event horizon is a small region, and does not extend to infinity (very free paraphrase, I can try to read the text more carefully if that isn't sufficient for you to reconstruct what he's doing).

4. Jan 5, 2010

### George Jones

Staff Emeritus
An event in spacetime is an element of a black hole region if there are no lightllike worldlines that start at the event and "end" at future null infinity. Future null infinity is (possibly) part of the boundary of conformally compactified spacetime. The boundary of a black hole region is an event horizon. The black hole region of Minkowski spacetime is empty, while the black hole region of Schwarzschild spacetime is non-empty. See Sean Carroll's notes starting at page 192 (pdf page 199),

http://arxiv.org/abs/gr-qc/9712019.

5. Jan 5, 2010

### yuiop

George has given a good answer, but I would like to add the following observations.

Consider the following chart of equally spaced rockets undergoing Born rigid acceleration in flat spacetime, which is equivalent to the worldlines of Rindler observers in Minkowski spacetime:

It has many similarities to Kruskal Szekeres coordinates except for the obvious lack of singularities in the top and bottom quadrants. As Hurkyl has already pointed out light can not escape from the top quadrant (the future light cone) and nothing can remain in the lower quadrant (the past light cone), but there is more. Any observer that falls off the accelerating rockets and freefalls ends up in the black hole region in the top quadrant. Also notice that accelerated observers in the left quadrant can not communicate with accelerated observers in the right quadrant and vice versa as long as they remain in their respective quadrants. In KS coordinates the left and right quandrants represent two separate universes and it is interesting that rockets accelerating in flat spacetime can aproximately simulate the event horizons of black and white holes and even more surprisingly can also simulate two universes.

These Born/Rindler rockets accelerate proportional to gm/r which does not fully duplicate the curved spacetime around a massive body. The really interesting stuff comes when you get the rockets to accelerate in a manner that duplicates curved spacetime with acceleration proportional to gm/r^2 and an offset of r=2m.

Last edited: Jan 5, 2010
6. Jan 5, 2010

### bcrowell

Staff Emeritus
Interesting question! I thought it was obvious, and then kept coming up with wrong answers :-)

I would feel more satisfied if I could find an answer less technical than some of the ones posted so far. This doesn't seem like it should be a problem requiring a highly technical answer.

One criterion for testing any proposed answer to your question is that it should work for all event horizons, not just the event horizons of black holes. E.g., it should work for the event horizon seen by an accelerated observer. As a corollary, the answer to your question should not involve any distinction relating to curvature of spacetime, since you can have horizons in flat spacetime.

A black hole's event horizon basically is very similar to a light cone, in the sense that you can make it out of a sheaf of lightlike world-lines. The event horizon of a black hole is a place where the light cones tip over so far that the entire future light-cone of any event is at radii closer to the center. I think all of this is true as well for the event horizon seen by an accelerated observer.

One clear distinction between a light cone and an event horizon is that a light cone can be defined locally, whereas an event horizon is usually defined in terms of the ability to escape to infinity. I think this is just a rephrasing of some aspects of the more technical answers, in less technical language.