Falling into a Black Hole: Blueshift Questions Explored

[Grasshopper]

TL;DR Summary

What does light from outside the black hole look to you as you fall in, along with the light?

I am under the impression that an outside observer would see things redshifted as the person they are observing approaches the event horizon. So, it seems reasonable that someone from inside the black hole would see incoming light blueshifted. Is this inaccurate? Why or why not?

If it is accurate, is there a point where the light is blueshifted so strongly that it kills the person (or gives them cancer or whatever)? But wouldn't this violate logic since the other observer sees the light redshifted (although clearly they can't see into the even horizon), so why would it kill the person? I'm assuming that blueshift and redshit are simply coordinate dependent phenomena, and have no true independent reality (much like what we see on a clock; differential aging is objectively real, but time dilation is coordinate dependent, given that two observers can measure the other observer's clock as slower than their own). But if in your reference fame, ultra-high-energy gamma rays are smacking you in the face, surely that can't be safe.

Another thing to consider, I think, is if the local spacetime around the observer is locally Minkowskian. If the black hole is large enough that tidal forces don't really matter locally, I can't see why not.
So, what happens here? Does the light coming into the black hole at you turn into ultra deadly high energetic rays? Or is it locally business as usual?
Last question: if the black hole is so large that tidal forces are irrelevant, will the blueshift or redshift also be small for the local observer inside the black hole? Why or why not?Thanks to all!

 

[PAllen]

What you need to realize is that all cases of red shift or blue shift in special and general relativity and even pre-relativity physics are a function of states of motion of the emitter and receiver. Curvature in general relativity in cases like gravitational redshift or cosmological redshift are best thought of as modifying which states of motion produce which spectral shift, but always, the state of motion of emitter and receiver are paramount.

For gravitational redshift, it is true that a stationary observer near a black hole horizon detects highly blue shifted light. However, such an observer is very special, in that infinite thrust is needed to maintain stationary motion on approach to a BH horizon. Meanwhile, a free faller into a BH is moving very fast relative to such a stationary observer, in the direction away from any distant emitter. Thus, they will see much less blue shift. When you actually perform the calculation, it turns out that a free faller starting from far away from the BH will actually see redshift from distant emitters rather than blueshift. If free fall begins closer to the BH, then moderate blueshift is seen at horizon crossing.

One other point - redshift and blueshift are absolutely not coordinate dependent. They are direct measurements by a detector, based on actual emission. It is impossible for the reading on a given instrument to be coordinate dependent.

 

[Grasshopper]

Ah yes, of course, you measure it, thus it is not coordinate dependent.

So, as you cross the event horizon, blueshift at best would be moderate.

Does this also depend on the size of the black hole? I am under the impression that tidal forces depend on the size (if altitude is the same, larger black hole means more gentle tidal forces), so is there a relationship to blueshift you'd see at the event horizon and size of the black hole?

 

[PAllen]

Ah yes, of course, you measure it, thus it is not coordinate dependent.

So, as you cross the event horizon, blueshift at best would be moderate.

Does this also depend on the size of the black hole? I am under the impression that tidal forces depend on the size (if altitude is the same, larger black hole means more gentle tidal forces), so is there a relationship to blueshift you'd see at the event horizon and size of the black hole?

No, tidal forces are not relevant to this case (assuming you can make a detector very small). The size of the BH matters only insofar as what counts as "close" versus "far" from the BH. Thus, for a supermassive BH, free fall from a stationary start from 1 light year away may be "close", and see blueshift on crossing, while for a stellar mass BH, it would be "far", and red shift would be observed. A little more technically, free fall starting from a point where there is still a large Newtonian gravitational potential difference relative to infinite distance, is "close", while if there is little potential difference, this is "far". Of course, this is all easily quantified in the context of the Schwarzschild geometry, but the Newtonian potential approximation is sufficient for general understanding.

 

[Ibix]

So, it seems reasonable that someone from inside the black hole would see incoming light blueshifted. Is this inaccurate?

For a hovering observer it's accurate - if I look up at you standing at the top of a ladder I see you faintly blueshifted and you see me faintly redshifted. If someone falls past me, though, they see you faintly redshifted compared to what I see because their kinematic redshift applies on top of the gravitational shift - so they might see you net redshifted or net blueshifted depending on their speed and the height difference. I believe that an observer free falling from rest at infinity sees light from above net redshifted - that is, the speed effect dominates.

Note that it isn't generally possible to split redshift into a "kinematic" and a "gravitational" component. It is possible in cases where there is a sense in which it's possible to define a "space" that doesn't change with "time", like Schwarzschild spacetime, but not in general. So this analysis is useful here, but be wary of relying on it.

 

[Grasshopper]

No, tidal forces are not relevant to this case (assuming you can make a detector very small). The size of the BH matters only insofar as what counts as "close" versus "far" from the BH. Thus, for a supermassive BH, free fall from a stationary start from 1 light year away may be "close", and see blueshift on crossing, while for a stellar mass BH, it would be "far", and red shift would be observed. A little more technically, free fall starting from a point where there is still a large Newtonian gravitational potential difference relative to infinite distance, is "close", while if there is little potential difference, this is "far". Of course, this is all easily quantified in the context of the Schwarzschild geometry, but the Newtonian potential approximation is sufficient for general understanding.

Okay so back to tidal forces and size: Am I mistaken that being close to a super massive black hole you’d feel gentler tidal forces than close to a stellar mass sized black hole? What about if you were at the event horizon for each?

 

[phinds]

Okay so back to tidal forces and size: Am I mistaken that being close to a super massive black hole you’d feel gentler tidal forces than close to a stellar mass sized black hole? What about if you were at the event horizon for each?

Close to the EH of a supermassive BH the tidal force would be tiny whereas near that of a small BH you would be ripped apart (if not already having been).

 

[Ibix]

Okay so back to tidal forces and size: Am I mistaken that being close to a super massive black hole you’d feel gentler tidal forces than close to a stellar mass sized black hole? What about if you were at the event horizon for each?

Imagine a centimeter-sized black hole near your stomach. It'd pull your head downwards and your feet upwards. On the other hand, a really huge black hole pulls your whole body in roughly the same direction - it can't be near your stomach and not near your head and feet.

So yes, the tidal effects near the horizon of a small black hole are more significant than for a large black hole.

 

[PeterDonis]

it seems reasonable that someone from inside the black hole would see incoming light blueshifted. Is this inaccurate?

Yes. It is impossible for someone inside the black hole to be stationary; they must be falling inward. The falling inward means they will see incoming light as redshifted.

 

[PeterDonis]

For a hovering observer it's accurate

But the OP asked about someone inside the black hole, and inside the hole there are no hovering observers.

 

[Ibix]

But the OP asked about someone inside the black hole, and inside the hole there are no hovering observers.

Ah yes - missed the "inside" bit. So you can't do the kinematic/gravitational split for such observers.

 

[PAllen]

I thought it worth quantifying an observation I previously described. Imagine dropping detectors into a BH from various Schwarzschild radial coordinate values. There is a particular r value such that there is no spectral shift seen by the detector from radially distant sources at horizon crossing. A detector dropped from further away will see red shift, and from closer will see blue shift. The r value of this neutral shift is directly proportion to BH masss.