Quote:
Originally Posted by Jeffocal
Thanks 
However you will have to explain to me using only the concepts of relativity why the center of a star is consider to have greater gravitational potential than its surface because until then I will stick to the conclusion both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.
Please try to explain it to me in terms of the relativistic properties the star internal gravitational potential not relative to anything outside of it. |
No problem. First, I should add that I edited that post right before you replied to it. I meant to say:
But, time dilation is a function of gravitational potential and the person at the center of the star has greater potential [where potential (U) is considered positive] than the person on the surface. The further from the center of the star, the less the potential and the faster clocks run.
rather than slower.
But, yeah, gravitational potential energy can either be negative or positive. In Newtonian mechanics it is considered negative and called phi (
), or V. In general relativity it is considered positive and called U. It doesn't really matter which way you do it, it's just important to keep straight which sign you're using.
Probably the easiest way for me to convince you that potential is greatest at the center of the object and decreases to zero at infinity is to quote a good source:
So, if you look at that blue line it is most negative (in general relativity we would say it is "most positive") at r=0, the center of the solid sphere. That's the point where time dilation would be greatest and clocks would run slowest. The higher up the blue line goes on the graph the less time dilation we have and the faster clocks run.
The field strength which is the slope of that blue line at any given point is not the same as the potential. The value of potential at a point on the line is given by how far up and down on the graph the point is. In particular, at r=0 (the center of the sphere) the slope is zero meaning the field strength is zero, but the potential is not zero.
You'll find that result is fully derived on that web page:
Gravitational potential due to rigid body. We would say, then, that gravitational potential is zero at infinity and increases as one gets closer to a massive body. It continues to increase inside the body and is largest at the center of the mass. The larger the potential, the slower clocks tick.
~modest
