Exploring the Effects of Black Hole Gravity: Blueshift

[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.