Why can't light return from a black hole?

[Dephenistrator2]

So if light is "pulled" into a black hole by following the curvature of seriously bent space time. Then i question, why does it not eventually come back out the other side? If its not literally being dragged in then shouldn't it ride through the whole thing and eventually come back out? From this perspective it either hints at deeper mechanics of black holes or light.

 

[Simon Bridge]

In GR it is all about geometry ... light does not come back out because the geometry won't let it.
One way some people like to think about it is that space-time is getting sucked into the black hole faster than the light can travel. It's like a mouse on a rug that is being pulled towards the cat faster than the mouse can run. But that's not really that great an analogy - to get the subtlety you need to learn the maths.
The simple answer is that light cannot get away from a black hole because it just does not have enough energy to do so ... it's the same reason objects traveling slower than escape velocity of their position wrt the Earth cannot escape the earth.

 

[Dephenistrator2]

Thank you for the response. If I'm getting this anology, space is stretching so fast in the center of a black hole that light cannot make up the difference and it is essentially trapped? The analogy for objects escaping Earth has a similar speed degradation, but that has gravity drawing its mass back down to earth. If light is not effected by gravity then the black holes pull shouldn't matter and the wavelength of light could theoretically ride through the black hole. Of course this is all moot if the rapid stretching is true.

 

[Simon Bridge]

It is true that light is affected by gravity ... the rest follows if you add the relativity wrinkles in (invarient speed for light, indistinguishability of inertial frames, indistiguishability of gravity and acceleration)
https://en.wikipedia.org/wiki/Black_hole

With relativity you have to be really careful - you have to say who is watching and where and what they are looking for.
Consider an experiment - someone a long way from the com of a black hole fires pulses of light towards it, varying the angular deviation from dead-on, and timing how long it takes for the light to arrive at the same radial distance as it started. Got it?

As the projected trajectory gets closer to the even horizon, the time of flight gets longer ... should the trajectory cross the event horizon, the time is infinite.
From this POV the light pulse had to traverse increasingly long distances through space. But from that POV, in that simple model, the light never crosses the event horizon in the first place: if it never gets in it cannot get out.

There are lots of ways to look at it:
To really get it - derive the field equations and then the solution for a massive sphere.
http://www.academia.edu/3518605/Deriving_Einsteins_Field_Equations_of_General_Relativity

 

[Dephenistrator2]

I had previously heard light not being effected by gravity save for altering its course by bending space, if it does tug light then that first sentence answers my question. I appreciate the rest of the explanations but i have a strong understanding of GR and black holes. I do have a weak understanding of the properties of light and its behavior, due to a horrible lack of decriptions I've been patchworking together and have curiosities of its limits. I had read a year ago about a scientist who suggested dark matter could be from a galaxies glow of light in ways other than normal mass in 2005 i believe? Heard he was disproven then, and had a resurgence of the theory some years later that was untestable. So this got me curious and caused this thread

 

[Simon Bridge]

In GR, there is no such thing as the force of gravity... which is to say: nothing is affected by gravity "save by altering its course by bending space". I'm afraid a "strong understanding of GR" requires an understanding of light since light rays are a core concept defining space-time. Also requires maths.

Perhaps:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC223005/
Basically, light travels on null geodesics.
https://en.m.wikipedia.org/wiki/Geodesics_in_general_relativity

 

[Nugatory]

So if light is "pulled" into a black hole by following the curvature of seriously bent space time. Then I question, why does it not eventually come back out the other side? If its not literally being dragged in then shouldn't it ride through the whole thing and eventually come back out? From this perspective it either hints at deeper mechanics of black holes or light.

When spacetime is curved a straight line can do strange things. For example, when you travel in a straight line on the curved surface of the earth, if you go far enough you'll end up back where you started. When you draw two parallel straight lines on the curved surface of the earth, if you extend them far enough they will intersect even though parallel lines aren't supposed to intersect. When you draw a triangle on the curved surface of the earth, you'll find that the sum of the interior angles is more than 180 degrees, although that shouldn't happen when you connect three points with three straight lines. And that's just curved space, not even curved spacetime.

Now, light always travels in a straight line in curved spacetime, but as the examples above show, straight lines in a curved space can behave in strange ways. Inside the black hole, the straight lines in spacetime followed by light (and the straight lines followed by free-falling objects, and the not-so-straight lines followed by powered spacecraft trying to escape) all lead to the singularity at the "center" of the black hole. So the light doesn't come out the other side because there is no path out - no matter what direction a light flash is moving inside the event horizon, it ends up at the singularity instead of passing through the horizon to the outside.

You may have noticed that I put the word "center" in scare-quotes. That's because "center" tempts us to think of the interior of the black hole as a sphere with a singularity in the middle, sort the way that a cherry or olive or similar fruit is a sphere with a seed in the center. It's not. We're talking about lines in spacetime, not just space, and once you are inside the horizon you are separated from the singularity not by space but by time so the singularity isn't in a different spatial position from you, it is in your (not very distant) future. You cannot help but reach it, for the same reason that you cannot help but arrive at noon sometime after 11:00 AM.

 

[Smattering]

Thank you for the response. If I'm getting this anology, space is stretching so fast in the center of a black hole that light cannot make up the difference and it is essentially trapped? The analogy for objects escaping Earth has a similar speed degradation, but that has gravity drawing its mass back down to earth. If light is not effected by gravity then the black holes pull shouldn't matter and the wavelength of light could theoretically ride through the black hole. Of course this is all moot if the rapid stretching is true.

Well, apart from all the obvious differences, light has one thing in common with a train: It travels on rails, and the rails on which light travels are called the geodesic lines of spacetime. Thus, in order to escape a black hole, light would require a geodesic line of spacetime that leads out of it. But there are none. And thus, the light is trapped.