Why does mass bend spacetime in a single plane?

[neildownonme]

well yeah i understand that in general theory of relativity is about bending of space time. but why does the bending of spacetime itself is not relative? i mean look at these photos,
why does spacetime was bended that way? why not sidewards? why not on top?
just want to know why. thanks :)

 

[Mark M]

Welcome to PF!

Spacetime curves in all dimensions. Those pictures are meant to provide a visual analogy.

Here is a better image.

 

[jtbell]

why does spacetime was bended that way?

People make diagrams like that because they don't know how to make diagrams of curved four-dimensional spacetime on a two-dimensional sheet of paper (or computer screen). Do you?

 

[neildownonme]

Welcome to PF!

Spacetime curves in all dimensions. Those pictures are meant to provide a visual analogy.

oh wow that's really a better picture :)
but why do planets spiral in a single plane then?

 

[espen180]

Beause of conservation of angular momentum. Deviation from a plane orbit in a two body system would imply a changing angular momentum of the system.

 

[neildownonme]

Beause of conservation of angular momentum. Deviation from a plane orbit in a two body system would imply a changing angular momentum of the system.

ahh, that all makes sense now. thanks a lot! :)

 

[Cleonis]

[...]
but why do planets spiral in a single plane then?

The curvature of space (as part of the spacetime curvature) is spherically symmetric around the source.
Spherically symmetric: there is no force component away from the instantaneous orbital plane. So planets remain in the same orbital plane

The orbits being planar goes back to the (spherical) symmetry.