Does Density Influence the Curvature of Spacetime?

[PhyHunter]

Does Density of matter can affect spacetime ? I want to say two same mass but volume is different, this time can we say density of matter affects spacetime different?

thanks!

 

[Dale]

Does Density of matter can affect spacetime ? I want to say two same mass but volume is different, this time can we say density of matter affects spacetime different?

Your question is a little unclear. Energy density is the time-time component of the stress-energy tensor in local inertial coordinates (http://en.wikipedia.org/wiki/Stress–energy_tensor), and that is dominated by ρc². Then the stress-energy tensor affects spacetime according to the Einstein field equations (http://en.wikipedia.org/wiki/Einstein_field_equations).

 

[1977ub]

If we take a symmetric sphere and nearly all mass is concentrated at the center, vs a case where nearly all mass is distributed along the surface, the Newtonian gravitational force experienced is the same comparing the two cases for a point located anywhere outside of the sphere, correct? And does this also go for GR gravity & time dilation?

 

[Bill_K]

Yes, BUT. General Relativity does have a Gauss' Law for spherical symmetry, similar to the one for Newtonian gravity, but remember that the source of gravity in GR is not rest mass but energy.

In your example if you take N atoms and rearrange them, first in a shell and then concentrated in the core, their energy will be different, hence the gravitational field they produce will change. Supporting the shell will require elastic energy as well as gravitational potential energy.