Does Black Hole Gravity Cause a Blueshift in Approaching Light?

[jartsa]

Also, to hover that close to a black hole's horizon, you need a rocket with an extremely powerful engine and lots and lots of fuel, since the rocket thrust required will be enormous. The effects you describe are best viewed as due to the enormous rocket thrust, not due to the radiation itself.

Oh yes, if a spaceship is equipped with a ridiculously powerful engine, turning on a light bulb on the ceiling will cause a filament shaped hole to appear on the floor.

 

[PeterDonis]

if a spaceship is equipped with a ridiculously powerful engine, turning on a light bulb on the ceiling will cause a filament shaped hole to appear on the floor.

If the ship's acceleration is large enough relative to its height that the blueshift from ceiling to floor is that large, yes. But that is a much more stringent condition than what is required for the ship to hover close enough to a black hole that radiation coming in from far away is blueshifted to that extent. A ship in the latter situation could still have negligible blueshift over the range of its own height.

 

[Revolucien]

Let's say I start shining a laser pointer down towards a black hole. One meter above the event horizon there is a hovering mirror that reflects the light back. When I see the reflected light I turn the laser pointer off.

Now I calculate that the total number of produced waves was 10²⁰. And all those waves were in the space between me and the mirror when the first wave returned.

Next the experiment is repeated, but this time the mirror is one micrometer above the event horizon. This time 10²³ waves can be calculated having been between me and the mirror.

Well, it seems like in the latter experiment thousand times more waves were packed between me and the mirror compared to the first experiment.

(It took thousad times longer time for the light to return in the second experiment, because of Shapiro delay)

Jartsa,
Your experiment got me thinking and curious about what happens if the mirror is now 1 micro meter past the EH? Is the EH the critical point where space time dilation increases the path length beyond the photons ability to return?

 

[PeroK]

Jartsa,
Your experiment got me thinking and curious about what happens if the mirror is now 1 micro meter past the EH? Is the EH the critical point where space time dilation increases the path length beyond the photons ability to return?

You can't have a mirror hovering below the event horizon. Anything below the EH follows a path to the singularity.

Instead, you could think about someone falling through the EH and shining light in all directions. At the EH, light shone radially outward would theoretically hover at the EH indefinitely. Light in all other directions would follow a path inward towards the singularity. And, once below the EH, all light paths lead to the singularity. There are no light paths starting from inside the EH that cross the event horizon.

 

[timmdeeg]

I would like to add that a photon emitted inside the black hole upward "falls" towards the singularity. So even emitted upward it's r-coordinate decreases.

EDIT I just recognized @PeroK said the same: "And, once below the EH, all light paths lead to the singularity. "

 

[Android Neox]

From the perspective of an observer at any point in space above a black hole's event horizon, stationary with respect to the black hole, the blueshift of a light beam shown down to the event horizon would be infinite. By the time the front of the light beam reaches the event horizon, the light beam (imagine an idealized laser beam) would contain an infinite sequence of light wave cycles.

 

[PeterDonis]

From the perspective of an observer at any point in space above a black hole's event horizon, stationary with respect to the black hole, the blueshift of a light beam shown down to the event horizon would be infinite.

This doesn't make sense; the observer you're talking about is emitting the light beam, not receiving it. But "blueshift" means observed blueshift, i.e., blueshift observed when the beam is received. It's impossible to have an observer stationary exactly at the horizon to receive the beam.

 

[timmdeeg]

From the perspective of an observer at any point in space above a black hole's event horizon, stationary with respect to the black hole, the blueshift of a light beam shown down to the event horizon would be infinite

An observer stationary above the horizon would observe finite blueshift and another observer at the horizon wouldn't observe infinite blueshift because he can't be stationary there. He would be in free fall instead and thus would observe this light beam (source far away) redshifted with z = 1.

 

[PeterDonis]

another observer at the horizon wouldn't observe infinite blueshift because he can't be stationary there. He would be in free fall instead and thus would observe this light beam (source far away) redshifted with z = 1.

Note that there is no requirement that an observer crossing the horizon be in free fall. He could be firing his rockets and accelerating. He just can't possibly fire his rockets hard enough to stop at the horizon.

Also, the redshift of z = 1 for radially ingoing light from infinity, strictly speaking, is for a Painleve observer crossing the horizon, i.e., an observer who free-falls "from rest at infinity". Observers who free-fall from rest at a finite altitude will have a different 4-velocity when crossing the horizon so the redshift they observe won't be exactly z = 1.

 

[timmdeeg]

Got it, thanks.