# B Conundrum thinking about crossing an Event Horizon

#### Grinkle

Gold Member
Folks usually point out that tidal forces make questions like the one I am asking below hypothetical at best, I understand that.

I am taking as an axiom that a free-falling observer observes nothing unusual when crossing an event horizon. More strongly, the free-falling observer cannot detect in any way that they have crossed an event horizon. If this isn't true, perhaps the reason why it isn't true answers my question.

From this lack of consequence to crossing an EH does it follow that as far as the free-falling observer is concerned, they haven't crossed any EH? How would they know that the singularity has now become an inevitable event for them? For a human observer curious to know if they crossed an EH, what consequence could they check for?

#### Exidor

They could see if their wristwatch broke?

#### russ_watters

Mentor
From this lack of consequence to crossing an EH does it follow that as far as the free-falling observer is concerned, they haven't crossed any EH? How would they know that the singularity has now become an inevitable event for them? For a human observer curious to know if they crossed an EH, what consequence could they check for?
What they know depends on what sources of information are available to them. The most obvious would probably be that they lost communication with remote observers. But as far as I know, there's nothing they can do inside the spaceship that would tip them off.

#### Ibix

"I can't detect it" doesn't mean it hasn't happened. An infalling observer does cross the event horizon, and the event horizon is a well-defined surface in spacetime. There isn't any "for me" about it - you are inside or outside.

One simple way to determine whether you've crossed the horizon is to work out where it is by observing orbits before you drop through it. Then you can use timing or observation of marker buoys to determine when you've dropped through.

I suspect if you watch incoming starlight it may be enough to locate the horizon. All the stars will shift to a small patch of sky above you as you approach, and the angular range may be enough to determine when you've reached the horizon. Not sure - you may also need the hole mass in advance.

But in local terms, there's no way to detect horizon crossing, no.

#### Exidor

If they looked behind them, the stars and everything else would be redshifted to the point of blackness.

#### Ibix

What they know depends on what sources of information are available to them. The most obvious would probably be that they lost communication with remote observers. But as far as I know, there's nothing they can do inside the spaceship that would tip them off.
Depends what you mean. Outside sources would always be able to communicate to them, and they would always be able to communicate with other infalling observers. They would not be able to answer non-infalling sources outside the hole, true.

#### Exidor

At the event horizon has the object reached a velocity of C?

#### Ibix

If they looked behind them, the stars and everything else would be redshifted to the point of blackness.
Some care is needed here. The Doppler shift depends on the infaller's velocity, so there is no unique value of Doppler that identifies horizon crossing. I'm also not certain that the stars are red-shifted, but I will check.

#### Ibix

At the event horizon has the object reached a velocity of C?
No. First - speed relative to what? A local description of crossing the horizon is that the horizon passes through you at c. But no local observer will see you doing c. A global description doesn't really have a well-defined notion of velocity except to refer you to particular families of local observers - who cannot see you doing c.

#### Exidor

Looking at the black hole from outside the event horizon everything at the event horizon and closer to the center of the black hole would appear black, wouldn't it? Is this the same as an infinite red shift?

#### Grinkle

Gold Member
Outside sources would always be able to communicate to them
If there were a pinging beacon outside the EH (say in some stable orbit around the black hole) that the traveler was monitoring, will the ping frequency combined with knowledge of the beacon orbit and the mass of the black hole tell the traveler when they have crossed the EH? I am thinking, perhaps incorrectly, that the traveler will observe the ping frequency increasing as they go deeper into the gravity well.

#### Ibix

Some care is needed here. The Doppler shift depends on the infaller's velocity, so there is no unique value of Doppler that identifies horizon crossing. I'm also not certain that the stars are red-shifted, but I will check.
My calculations suggest stars are blueshifted for an infalling observer.

I wrote down a tangent vector to the worldline of a radially infalling massive observer and a radially infalling light pulse. The inner product should be proportional to the measured energy of the light, and hence its frequency. This appears to be an increasing quantity, at least as far as the horizon.

Edit: I may have a sign error - need to recheck.

Edit2: I did - this post is incorrect

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#### Grinkle

Gold Member
Looking at the black hole from outside
I think the traveler will always see only black in front of them, even after they cross the EH. If that is not the case, I am very confused.

#### Ibix

Looking at the black hole from outside the event horizon everything at the event horizon and closer to the center of the black hole would appear black, wouldn't it? Is this the same as an infinite red shift?
Light does not come from the horizon, so defining the redshift of something that isn't there seems problematic to me.

#### Exidor

I would think it would slow down because of Doppler shift. But you also have time dilation as the observer approached C?

#### Ibix

If there were a pinging beacon outside the EH (say in some stable orbit around the black hole) that the traveler was monitoring, will the ping frequency combined with knowledge of the beacon orbit and the mass of the black hole tell the traveler when they have crossed the EH?
Probably. I'd need to switch to coordinates that don't fail at the horizon to answer this, and that's more maths than I'm going to do now - have to help with food prep...
I am thinking, perhaps incorrectly, that the traveler will observe the ping frequency increasing as they go deeper into the gravity well.
Based on #12, that would be my guess.

Edit: ...but #12 is wrong. See below.

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#### Ibix

I would think it would slow down because of Doppler shift. But you also have time dilation as the observer approached C?
That's one way to look at it. Another is to note that the infalling light gains energy from the gravitational potential so is blue shifted - apparently more than the kinematic redshift from the observer's increasing infall speed.

#### Exidor

Does the edge of a black hole show blue shifting of light in astronomical observations?

#### Exidor

I was thinking inside a black hole C is exceeded but time becomes imaginary.

#### Ibix

Does the edge of a black hole show blue shifting of light in astronomical observations?
I'm not aware of one being directly imaged. Why would you expect it to blueshift? We're not infalling observers. And what are you actually looking at? Light from the accretion disc (would be redshifted) or grazing light from stars behind (no effect for a non-rotating hole)?
I was thinking inside a black hole C is exceeded but time becomes imaginary.
I'm afraid this makes no sense.

#### skeptic2

"My calculations suggest stars are blueshifted for an infalling observer." - Ibex

Consider two free falling objects, one after the other. As they fall, the distance between them constantly increases due to the first object always falling faster than the second. To the first object, the second is receding from it, so it would appear to be red shifted. To a stationary observer, yes, the stars would appear blueshifted, but not to an infalling observer.

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#### Exidor

Well your saying that light coming towards a black hole is blue shifted. If this is the case then some of it would escape and appear at the edge of a black hole in an actual observation?

I am rusty but if you let v exceed c:
1/((1-(v^2/c^2))^(1/2))
The result is imaginary.

#### PeterDonis

Mentor
My calculations suggest stars are blueshifted for an infalling observer.
You should check your calculations. Ingoing light is redshifted for infalling observers.

the infalling light gains energy from the gravitational potential so is blue shifted
Relative to static observers (observers hovering at a constant altitude).

apparently more than the kinematic redshift from the observer's increasing infall speed.
No. See above.

#### Ibix

My calculations suggest stars are blueshifted for an infalling observer.

I wrote down a tangent vector to the worldline of a radially infalling massive observer and a radially infalling light pulse. The inner product should be proportional to the measured energy of the light, and hence its frequency. This appears to be an increasing quantity, at least as far as the horizon.
As noted, I made a sign error (accidentally switched to -+++ for the metric) and missed a sanity check (my energy was negative everywhere) that would have detected it. Incoming light is redshifted for an observer free-falling from infinity.

This isn't quite true for observers released from rest close to the hole, who see light blue shifted at rest. Light doesn't instantly become redshifted compared to its source frequency when the observer is released, but it is redshifted compared to the at-rest observation and the redshift grows as they infall.

#### PeterDonis

Mentor
Incoming light is redshifted for an observer free-falling from infinity.
Yes, agreed.

This isn't quite true for observers released from rest close to the hole
Yes, that's correct; an observer released from rest at a finite height will see a decreasing blueshift, then a switch to redshift and an increasing redshift. How long it takes them to see the switch depends on how close they are to the horizon.

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