Q: Black hole event horizon vs distortion effects

[Chris G]

Hello!

I'm having a hard time finding realistic black hole simulations, but I saw one recently (black hole size comparison on youtube) that showed the following 3 black holes (attached).

I noticed that the larger the black hole, the smaller the "distortion zone" was relative to the radius of the event horizon.

Was this simulation accurate? I had imagined that the distortion zone relative to the event horizon radius always remained the same before I saw this.

Thank you!

 

[PeterDonis]

Can you give a link? I can't tell from the image what the simulation is doing.

 

[Chris G]

Here is the link to this video:

 

[PeterDonis]

Here is the link to this video

Is this the video that the images are from? If so, a YouTube post is not a useful source; I need something that describes how the size of the "distortion zone" is being determined.

 

[Chris G]

Peter,

That is why I'm asking this question - there seems to be a lot of spacetime graphs out there or other representations (like this video) that show the idea of a gravity well funneling downwards, but that don't have realistic spacetime curves. This is the classic example:

So I'm asking specifically about how to determine the spacetime curve, or if somebody can link me to a realistic example of small vs large black hole spacetime curvature.

To ask my question a different way, please see my diagram below. Which is more realistic, example A, or example B?

 

[PAllen]

I spent a bit of time trying to find any sourcing for the images in that YouTube video, but could not find anything. I checked several reputable sources of imaging for black holes, and could find nothing similar to these images. Without some better reference, I don't see a way to discuss this. Note that actually generating such images accurately is a significant project, so no one here is going to be in a position to answer this question from first principles.

 

[Chris G]

I'm digging too - I feel like this is one of the most accurate simulations:
http://www.vis.uni-stuttgart.de/index.php?id=2460

This is another:
http://inspirehep.net/record/824061

These don't answer my question yet because I can't see relative sizes, but I feel like I'm getting closer.

 

[PeterDonis]

how to determine the spacetime curve

If you're interested in what the spacetime geometry looks like, none of the diagrams or videos you have linked to will help. They all show space, not spacetime.

The geometry of spacetime is four-dimensional, so we can't visualize it directly. But spacetime curvature is the same thing as tidal gravity, so if you imagine how tidal gravity acts on freely falling objects, you are imagining spacetime curvature. For example, objects separated radially will diverge due to tidal gravity, so spacetime curvature along the radial dimension (more precisely, along the "time-radial" dimension, since "diverge" means "separation increases with time") is negative; whereas objects separated tangentially will converge due to tidal gravity, so spacetime curvature along the tangential dimensions is positive. (This is for a spherically symmetric massive object.)

please see my diagram below

This still shows space, not spacetime.

 

[PeterDonis]

I feel like this is one of the most accurate simulations

Still shows space, not spacetime.

This is another

This one is of something completely different from the topic of this thread. (Did you notice the phrase "five-dimensional coalescing black hole solutions"?)

I feel like I'm getting closer.

I'm not so sure, since none of these show spacetime, and none of them explain how the "distortion distance" is calculated.