Multiple curves in space-time?

• B
When you put a mass on a trampoline it causes the trampoline to V. If you put another similar or same sized mass on the same trampoline at a great enough distance, will the curve on the trampoline/space-time look like a W or a U ?

If you can get the curves on a trampoline/space-time to look like W with the two masses spaced far enough apart. If you push mass_A towards mass_B will the curve peak between the masses (W) cause moving mass_A to repel/move mass_B?

If you add more mass gradually to mass_A side will it push mass_B away at first, until the curve peak between them comes down and then eventually they’ll start attracting or moving towards each other?

When you put a mass on a trampoline it causes the trampoline to V. If you put another similar or same sized mass on the same trampoline at a great enough distance, will the curve on the trampoline/space-time look like a W or a U ?

If you can get the curves on a trampoline/space-time to look like W with the two masses spaced far enough apart. If you push mass_A towards mass_B will the curve peak between the masses (W) cause moving mass_A to repel/move mass_B?

If you add more mass gradually to mass_A side will it push mass_B away at first, until the curve peak between them comes down and then eventually they’ll start attracting or moving towards each other?

Unfortunately you cannot say any of these things, as the trampoline analogy is simply not realistic; there are many sources on the internet that will tell you this. Here is one.

Nugatory
Mentor
You can't just add mass in general relativity, it has to come from somewhere. Thus there's no way for general relativity to tell us what would happen if a mass were to appear from nowhere - it's like asking a mathematician what would happen if we found an odd number that's an exact multiple of two.

@m4r35n357 has already pointed out that the trampoline is a bad analogy for the curvature of spacetime. If you search this forum for posts by member @A.T. you'll find a video he's made which shows a much better way of visualizing the way that curved spacetime leads to gravitational effects.

PeroK
Homework Helper
Gold Member
2020 Award
When you put a mass on a trampoline it causes the trampoline to V. If you put another similar or same sized mass on the same trampoline at a great enough distance, will the curve on the trampoline/space-time look like a W or a U ?

If you can get the curves on a trampoline/space-time to look like W with the two masses spaced far enough apart. If you push mass_A towards mass_B will the curve peak between the masses (W) cause moving mass_A to repel/move mass_B?

If you add more mass gradually to mass_A side will it push mass_B away at first, until the curve peak between them comes down and then eventually they’ll start attracting or moving towards each other?

Leaving aside the issue of the rubber sheet, there is an important point here. Whatever your theory of gravity it must match the experimental evidence. A question like this is already answered if you think of the Solar System:

The planets orbit the Sun
Some planets have moons (or artificial satellites) that orbit them
A projectile fired on the Moon will travel in a parabola before returning to the surface of the Moon

That's the way gravity behaves, regardless of the theory that explains it. In particular, there is no experimental evidence for masses ever repelling each other. And, in fact, Newton's law of gravitation is sufficiently accurate to model the Solar system. So, whatever GR says, it must be very close to Newton's gravity on the scale of the Solar System.

If you can get the curves on a trampoline/space-time to look like W with the two masses spaced far enough apart. If you push mass_A towards mass_B will the curve peak between the masses (W) cause moving mass_A to repel/move mass_B?

If you add more mass gradually to mass_A side will it push mass_B away at first, until the curve peak between them comes down and then eventually they’ll start attracting or moving towards each other?
In addition to what’s been said about how the rubber sheet is a poor analogy for gravity (or at least very, very, very limited in its application), your ideas about trampolines are incorrect. The peak in your “W” will shrink until the masses converge.

A.T.

Mister T