Aid to visualizing warped Spacetime?

[EskWIRED]

I've wanted a visual aid to the curving of spacetime and I can't seem to find one.

What I am thinking about would be a 2D simulation of a 3D grid, a matrix, made up of evenly spaced lines. Initially, it would simulate flat spacetime, composed of cubes with grid lines at all the intersections. Just a picture of transparent empty boxes.

But I envision an attractor which the user can place in the grid. The attractor would attract the lines, and bulge the boxes towards the attractor.

The bulges would simulate the effect of gravitational curvature on spacetime. What would result would be a picture of the transparent boxes subject to tidal forces, varying from extreme close to the attractor, and nearly insignificant if one were to zoom out far from the attractor.

Does my description of what I have in mind make sense?

If so, would it really be a visual aid to curving space time? Only curving space? Neither?


I would also envision user input to vary the "mass" and the "radius" of the attractor, enabling one to create white dwarfs, neutron stars and black holes.

What I really want to do is to set things in black hole territory, and see what happens to the "shape of space" in the vicinity.

Further refinements could include rotation of the attractor with consequent frame dragging, multiple attractors showing a frozen slice of time, or even multiple moving attractors warping space into weird shapes, with low-mass objects flying through.

Does anything like this already exist?

 

[bcrowell]

I think what you're describing would have the limitation that it could only visually represent spatial curvature. The Riemann tensor doesn't just have space-space elements in it. It also has time-space elements.

Also, keep in mind that an animation like the one you're describing can be misleading, because each frame seems like one snapshot in time, whereas there is no such notion of simultaneity in GR. This is a big issue, e.g., when you deal with black holes, where there is no such thing as a static observer inside the horizon, and the Schwarzschild "r" coordinate becomes timelike.

Further refinements could include rotation of the attractor with consequent frame dragging, multiple attractors showing a frozen slice of time, or even multiple moving attractors warping space into weird shapes, with low-mass objects flying through.

Doing this exactly would be extremely complex, since you'd have to include effects like gravitational radiation.

A couple of the links in this thread have animations: https://www.physicsforums.com/showthread.php?t=632575

 

[A.T.]

Some related links here:
https://www.physicsforums.com/showpost.php?p=4053568&postcount=2

 

[EskWIRED]

I think what you're describing would have the limitation that it could only visually represent spatial curvature. The Riemann tensor doesn't just have space-space elements in it. It also has time-space elements.

Thanks. I can understand that limitation.

But given the limitation, would such a gadget, in its simple form, with only one static attractor, produce a decent enough simulation of the effects of curved space visually?

ISTM that each of the cubes would be deformed towards the attractor, much in the manner that space is "attracted" by gravity. And if the proper formulas were used for the characteristics of the attractor, it might be of great aid in visualizing what happens to space in the vicinity of a massive object.