GR - time dialation at center of a planet

[rcgldr]

The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

 

[George Jones]

The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

See

https://www.physicsforums.com/showthread.php?p=1543402#post1543402.

You might want to set $v=0$.

See also,

https://www.physicsforums.com/showthread.php?p=1836071#post1836071.

 

[A.T.]

The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

Gravitational potential minimal -> clock rate minimal

Here is a visualization of the complete Schwarzschild metric (interior + exterior combined):

http://www.adamtoons.de/physics/gravitation.swf

 

[Al68]

The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

A clock at the center of a planet will run slow relative to a clock at the surface (neglecting rotational effects). Time dilation isn't caused by gravitational "force", it's the result of the difference in potential. Any object in between the surface and center of a planet would "freefall" toward the center in the absence of the forces acting on it (like the material resistance of the mass of the planet).

Light traveling toward the center would blueshift, and light traveling away from the center would redshift, just like it would above the surface. That's what determines gravitational time dilation, not the amount of gravitational "force" acting on the clock.

 

[rcgldr]

Thanks for the responses.