# Mass causes space time curvature

by shounakbhatta
Tags: curvature, mass, space, time
P: 2,470
 Quote by shounakbhatta The bigger the of the mass, the bigger the dent(curve) in the space time.
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.
Thanks
P: 3,669
 Quote by 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.
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....
 Like people have said, you shouldn't take the analogy with object on an elastic surface too literally.