Mass causes space time curvature

Naty1

Here is a nice discussion of relativity...
and some comments on curvature here:
http://math.ucr.edu/home/baez/einstein/node2.html

K^2

No. The metric for a non-rotating spherical body is a function of mass ONLY. If you go the same distance from center of the object with a fixed mass, you will find exactly the same curvature of space-time regardless of how dense the object is.

If the Sun was to be replaced by black hole of equal mass right now, all of the planets would keep on moving in exactly the same trajectories. In terms of gravity, we wouldn't notice the difference.

Like people have said, you shouldn't take the analogy with object on an elastic surface too literally.

Nugatory

Although if the object is denser, you can move closer to the center of mass while while still remaining outside the surface of the object where the vacuum solution is valid. Thus you can experience stronger gravitational and tidal forces and more curvature; this increase is probably what shounakbhatta was getting at when he spoke of a "bigger dent".

Which just goes to show....

K^2

If that's what he was looking for, then yes. But it sounded like he expected same curvature at the surface, but further out as object size increases, which isn't correct.

bahamagreen

Is the interior of a hollow sphere Ric=0?

K^2

Yeah, vacuum is always Ricci-flat.

bahamagreen

Would we say the interior of a hollow sphere is a case where mass causes space time non-curvature... in so far as additional regional curvatures will still be present within the sphere, but the sphere's regional curvature will contain a "flat spot"?

K^2

It's actually completely flat. The only spherically symmetric solution that is Ricci-flat and doesn't have mass at the center singularity will be flat. The interior will be time-dilated compared to exterior, but otherwise, identical to Minkowski space-time.