What caused time to run slower in a field of gravity

stevebd1

Schwarzschild interior solution-

http://www.physicsforums.com/showpos...02&postcount=8

rrogers

A crude method is to compute the Energy difference between the different positions. Similiar to what was done in the QM example.
The proper method in all cases is to integrate the "proper" distance as mentioned. In GR this would always be the proper time elapsed; this can also included null geodesics (which contribute nothing). The integration path doesn't need to be a geodesic. Typically intuitive type of reasoning can be fooled since we have little experience in these realms. GR is mathematically consistent, so we need to bring our intuition into line with what the mathematics says. Mathematical consistency says nothing about whether it matches reality though.

Ray

rrogers

Looks more or less okay, but are you sure about M/R ? I don't see the density term and I think you need it. For instance if M is constant then your last expression blows up.
Presuming that your original expression is right then the density should be the constant; OTOH constant density is a stretch for the earth. Although not for a meteor.

Ray

stevebd1

In the metric M is geometric (M=Gm/c^2), 2M being the schwarzschild radius of the object of mass and R being the overall radius of the object of mass. Based on this, as r tends to zero, R remains constant and none of the expressions appear to blow up. Which expression are you refering to?

rrogers

Okay, I will reexamine the result. It still seems strange to me that the expression uses Schwarzschild terms instead of density. The longer I think about the stranger it seems; probably a shortcoming on my part.


Ray

K.J.Healey

It comes from making the boundary conditions at the surface; going to the exterior solution (Pressure at surface goes to zero). By using the boundary conditions all of the unknwons will be solved for in terms of M enclosed and R boundary. (given the EOS)

rrogers

I presume you are using Florides solution. I will have to wait until I move into my house and have a real computer to do a real analysis. This little laptop running Vista is really trying.
Ray