Does the Black Hole Event Horizon violate the Equivalence Principle?

[Sigie]

My understanding is that, according to the Equivalence Principle, accelerated motion is indistinguishable from that of being in a gravitational field. So then, at the Event Horizon of a black hole, where gravity is too great for light to escape, wouldn't that be equivalent to accelerated motion at the speed of light(which is not possible)?

An outside observer watching something approaching an event horizon or an object accelerating at a relative speed approaching the speed of light would both observe the object slowing down. It would seem that they are equivalent.

 

[Garth]

Welcome to these Forums Sigie - an interesting question that will help resolve some possible sources of confusion.

The Einstein equivalence principle (EEP) is only valid in the immediate locality, sufficiently close to the observer, in which case ""we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)".

However at short distances (cms) away from the point in question tidal forces can be detected even in a weak field such as the Earth, which are the signature of a non-uniform gravitational field but NOT an accelerated frame of reference.

Hence it is inappropriate to apply the equivalence principle to an observer watching at a distance something approach the event horizon of a black hole and so there is no violation of the EEP.

Garth

 

[tiny-tim]

Welcome to PF!

Hi Sigie! Yes: welcome to PF!

The Einstein equivalence principle (EEP) is only valid in the immediate locality …
…
Hence it is inappropriate to apply the equivalence principle to an observer watching something …

Yes … the equivalence principle is like some jokes …

you have to be there! ​

 

[granpa]

supposedly any observer that is moving has a region far behind them from which photons can't reach them. beyond this point clocks would seem to the observer to be moving backwards (if he could see them which he cant).

personally I consider relativistic effects like this to be illusions (I don't believe clocks really run backwards) and I am not a big fan of black holes either. I leave it up to you to decide for yourself what to make of it all.

 

[tiny-tim]

supposedly any observer that is moving …

No, any observer that is accelerating.

 

[granpa]

No, any observer that is accelerating.

yes that's right. my bad.

 

[Sigie]

Thanks for the welcome and thanks for the replies

I didn't mean to imply the equivence principle applied to a distant observer. My question is meant to refer to an object at the event horizon of say a large enough black hole where the difference in tidal force is not an issue.

So, locally, the effects of gravitation are the same as that of an accelerated observer in flat space. The way I have heard it explained is that if a man in an elevator feel himself being pressed against the floor, there is no way for him to tell if this is because a planet is beneath him or a rocket ship on a cable attached to the elevator is accelerating above him because, locally, the effects are indistinguishable.

So (and I am sure I am missing something here), if he is in a graviational field so strong that light cannot escape, is that not equivalent to being acclerated beyond the speed of light?

Thanks again for the replies!

 

[granpa]

general relativity is not my thing. but here is my take on it.

imagine a line of stationary evenly spaced perfectly synchronized clocks along the x-axis and a stationary rocket at the origin. the rocket accelerates to velocity v. now in the rockets frame the clocks are no longer synchronized. the rocket accelerates to 2v. now the clocks are even more out of synch. now the rocket accelerates and continues to accelerate. the clocks continuously become more and more out of synch. the further away the clocks are in one direction the faster they tick. the further away they are in the other direction the slower they tick and eventually they even begin to tick backward. supposedly the same thing occurs in a gravitational field.

I see what you are asking though. your asking 'what does it mean to be AT an event horizon'?

 

[tiny-tim]

Hi Sigie!

So, locally, the effects of gravitation are the same as that of an accelerated observer in flat space. The way I have heard it explained is that if a man in an elevator feel himself being pressed against the floor, there is no way for him to tell if this is because a planet is beneath him or a rocket ship on a cable attached to the elevator is accelerating above him because, locally, the effects are indistinguishable.

Yes, that's right.

(or the elevator could just be in the rocket ship! )

My question is meant to refer to an object at the event horizon of say a large enough black hole where the difference in tidal force is not an issue.

So (and I am sure I am missing something here), if he is in a graviational field so strong that light cannot escape, is that not equivalent to being acclerated beyond the speed of light?

There's no such thing as being at the event horizon … either you're inside it, or outside.

If you're outside, then light, of course, can escape.

If you're inside, then, as I understand Schwarzschild coordinates, you're gong faster than light anyway (the speed of light becomes a minimum instead of a maximum) … but I know from experience that most people here disagree with me on that!