Can an Object Falling in Infinite Gravity Break the Speed of Light?

[phinds]

4200 parsecs away is still within our galaxy, where expansion does not happen.

OOPS. My bad. Thanks for that correction. I can add, but I can't multiply

We can see objects 4,200 Mpc away, but only in a state how they looked like several billion years ago. The border where we will never be able to see their current state is somewhere at this distance. They don't freeze in spacetime, but our view on them will freeze.

Hm ... I don't follow. How does our view of them freeze? Wouldn't they just fade into darkness with greater and greater redshift?

 

[ExecNight]

I would expect them to freeze and redshift into darkness because;

Well for conservation of information i would expect them to act like an object falling into the black holes event horizon. Otherwise, that would raise many questions. Like Stephen Hawking did back then

 

[mfb]

Hm ... I don't follow. How does our view of them freeze? Wouldn't they just fade into darkness with greater and greater redshift?

Into darkness, but also into slower evolution (as seen by us) due to the redshift. The effect is very similar to objects falling into black holes (as seen by outside observers), just on a completely different timescale.

 

[phinds]

Into darkness, but also into slower evolution (as seen by us) due to the redshift. The effect is very similar to objects falling into black holes (as seen by outside observers), just on a completely different timescale.

OK, that I understand. I think the fading to darkness would occur before the "freezing" got too severe, but I guess you could say that depends on the sensitivity of the instruments "seeing" the objects.

 

[xox]

If a a object is falling in a gravity field with infinitly long radius. can it eventually travel faster than the speed of light?

No, the coordinate speed of a test probe falling from infinity is:

$$v=c(1-\frac{r_s}{r}) \sqrt{\frac{r_s}{r}}$$ for $r>r_s$

where $r_s$ is the Schwarzschild radius of the "attracting" gravitational mass and $r$ is the radial Schwarzschild coordinate. So, $v<c$ for all $r>r_s$.

If the test probe is dropped from $r_0$ the formula becomes:

$$v=c(1-\frac{r_s}{r}) \sqrt{\frac{r_s}{r}-\frac{r_s}{r_0}}$$ for $r_0>r>r_s$

For light, the coordinate speed is:

$$v=c(1-\frac{r_s}{r})$$