Posted: Feb 27, 2011 4:32 pm
by twistor59
Xaihe wrote:CdesignProponentsist's answer seems to be in conflict with your answer. Is it too forward to ask you two to fight it out? :grin:

Well, it's 25 years since I did any relativity, but I'm pretty certain that at the centre of a massive body, clocks would be running slower compared to ones at a distance from the body.

Xaihe wrote:
twistor59 wrote:
Xaihe wrote:Since gravity is stronger at the surface of a planet than at the center of a planet, does that also mean spacetime is curved less at the center of the planet, or just that the gravitational effect is canceled? In the same effect, does time go slower or faster at the center of the earth than at the earth's surface? If spacetime is curved less due to this cancellation, what does this tell us about the goings on inside black holes?

Imagine you're in space and you watch a clock drifting towards the earth. You would see it ticking slower and slower as it approached the earth. If it carried onwards, sinking into the earth, then it would continue to tick slower and slower until it reached the centre. One way to think of it is that effectively it's sinking deeper and deeper into the potential well, and photons would have to work harder and harder to climb out of it, hence get more redshifted. The ticks of the clock are equivalent to the cycles of the photons.

The strength of the gravity is more related to the gradient of this potential, whereas for comparing clocks we want to compare the values of the potential at two separate points. So the local strength of the gravitational force is not relevant.

Xaihe wrote:
It makes sense, but isn't the redshift only dependent on the gradient of the potential? For instance, in the case of 2 equal mass bodies, one smaller than its Schwarzschild radius, the other larger. Would then the redshift be different for both objects, while they have the same total potential?

They might have the same potential in a Newtonian sense, but the potential we're interested in here is g00, the time component of the metric. The redshift, or the slowness of the ticking relative to clocks in the asymptotic region, becomes infinite at the horizon. That sure ain't the same in the 2 cases !