Shape of Space-Time: Warping Explained

[Fuinne]

It space time is able to be warped, what is the shape of it? If it doesn't have a physical shape how can it be warped?

 

[phinds]

"Warped" is an English language word that does a poor job of describing what's going on and it is mostly due to applying Euclidean Geometry to a construct (space-time) that is NOT Euclidean. In Riemann Geometry, which is what more appropriately describes space-time, things move in straight lines called "geodesics", which if looked at from a framework of Euclidean Geometry, appear curved or "warped".

 

[Dale]

It space time is able to be warped, what is the shape of it? If it doesn't have a physical shape how can it be warped?

The shape of spacetime is given by:
$G_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}$

This is the Einstein field equation. The left hand side describes the shape of spacetime and the right hand side describes the distribution of energy, momentum, and stress.

 

[Fuinne]

The shape of spacetime is given by:
$G_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}$

This is the Einstein field equation. The left hand side describes the shape of spacetime and the right hand side describes the distribution of energy, momentum, and stress.

So is it some sort of amorphous shape?

 

[Dale]

It is a shape determined by the distribution of stress energy. Different distributions give different shapes, as described above.

Also, we don't have English words for the shape of most 4D pseudo Riemannian manifolds. So we describe it mathematically by the metric $g_{\mu\nu}$ The metric is the shape of spacetime.