Undergrad How Does General Relativity Explain Gravity's Conundrum?

[Mohammad Hunter]

So the other day I saw a YouTube video on how gravity works according to general relativity.
From what I understand, objects bend space_time with their mass and create a shape which is close to a cone. Since objects only move forward in time through a straight line, the bent space_time makes the objects fall on each other.
But my question is: when you create a cone and draw a straight line on it, the line starts from a lower level, goes up and down again( I'm talking about the lines Einstein had in mind) which creates a problem... In the model, all objects start from what looks like the peak and descend down.
I don't understand two things:
1. The heavy object is located on the peak of the cone( right?) And when the straight line is followed, it does get close to the massive object but passes through and starts wandering away( to make it easier I assumed one object is not massive enough to effect the other here)
2. Don't both objects travel with the same speed through time?( Specially when the two objects have the same mass) If so, they should be staying still from each other's perspective.( Their relative velocity is zero) So while the objects are moving forward in time, the cone is moving forward with them. So no fall should be expected.

 

[Orodruin]

You are taking popular animations and illustrations a bit too seriously here.

Energy, momentum, and stress act as sources of spacetime curvature. (Note that the technical word is that spacetime is curved, not bent.) Spacetime is four-dimensional and that cannot be easily illustrated so popularisers make do with analogies and do what they can.

 

[Mohammad Hunter]

You are taking popular animations and illustrations a bit too seriously here.

Energy, momentum, and stress act as sources of spacetime curvature. (Note that the technical word is that spacetime is curved, not bent.) Spacetime is four-dimensional and that cannot be easily illustrated so popularisers make do with analogies and do what they can.

So many questions, I don't know if they're actually scientific but if I'm correct, curving should not be possible without bending... I've forgotten the term but it has to do with the shape of the object, you can't cover a ball with a piece of flat paper without creating overlaps. If the same rule applies to space-time, then some bending is expected maybe?
Also this is clearly out of my area of knowledge cause I don't know what "relativity of simultaneity" is.
Thanks for the answer, I'll read about relativity of simultaneity.

 

[Orodruin]

you can't cover a ball with a piece of flat paper without creating overlaps

This is neither curving nor bending. "Bending" has no well defined meaning in this context and "curved" has a very precise mathematical meaning. It requires no external space to be curved in as you are likely imagining it.

 

[phinds]

... curving should not be possible without bending

You are using Euclidean Geometry terms. This is not the proper math to use for spacetime (you need Riemann Geometry) and as Orodruin pointed out the terms as applied to space-time do not mean what you think they mean.

 

[A.T.]

So the other day I saw a YouTube video...

How about a link, so we know which one you mean.