Will photons fry an object falling into black hole?

[Ookke]

For outside observer, an object falling into black hole seems to freeze at event horizon and never cross the boundary and proceed inside the black hole. This is of course not the case in the falling objects own reference frame. Depending on the size of the black hole, a falling object may not even notice anything out of ordinary.

However, in an outside observer's reference frame, the object freezes at the event horizon and stays there forever, until the end of the universe. The falling object will be hit by enormous amount of photons, which are also blueshifted because of gravity at the black hole. No matter how far away, or how distant future, a photon with proper direction will reach the falling object at constant speed c and hit, because the falling object is still there waiting just above the event horizon.

Actually I don't think this is correct description of what happens, but I cannot specify any reason why this is incorrect. If the object stays there, and it's hit by photons until the end of the universe, it will fry. And if it does, it must do that in any frame (also in the falling object's own frame) because different reference frames cannot disagree about local events. This is contradictory to description that falling object may not notice anything special.

 

[DrGreg]

From the point of view of an outside observer who chooses to use a coordinate system in which a falling object almost freezes near the horizon, the photons approaching the object almost freeze as well.

in a non-inertial coordinate system the coordinate speed of light need not be c.

 

[PeterDonis]

in an outside observer's reference frame, the object freezes at the event horizon and stays there forever, until the end of the universe.

This is not incorrect, exactly, but it is easy to draw incorrect conclusions from it, as you do:

The falling object will be hit by enormous amount of photons, which are also blueshifted because of gravity at the black hole. No matter how far away, or how distant future, a photon with proper direction will reach the falling object at constant speed c and hit, because the falling object is still there waiting just above the event horizon.

No, this is not correct. To fully see why requires doing the math, but I can at least suggest one thing you've overlooked in your reasoning: if the falling object appears to "freeze" as it approaches the horizon, wouldn't photons appear to "freeze" as well? (If you actually do the math, you find that yes, this is exactly what happens: infalling photons that start falling in past a certain point of the outside observer's time never actually cross the falling object's worldline; more and more photons appear to "pile up" above the falling object, without ever catching it, as the outside observer's time goes further and further into the future.)

If the object stays there, and it's hit by photons until the end of the universe, it will fry. And if it does, it must do that in any frame (also in the falling object's own frame) because different reference frames cannot disagree about local events. This is contradictory to description that falling object may not notice anything special.

You're correct that if the object were to fry, all reference frames would have to agree on this. But the object doesn't fry (and all reference frames *do* agree on that, including the outside observer's--see above), so there's no contradiction with the fact that the falling observer should not notice anything special.

 

[Ookke]

if the falling object appears to "freeze" as it approaches the horizon, wouldn't photons appear to "freeze" as well?

Basically yes and I can accept it, but I was stuck in the thought that light speed must be invariant c. Also it seemed reasonable that an observer far away from black hole would have inertial coordinate system, but that's not the case as pointed out. Thanks for your answers.

 

[WannabeNewton]

Also it seemed reasonable that an observer far away from black hole would have inertial coordinate system, but that's not the case as pointed out.

Even if the observer is at spatial infinity in an asymptotically flat space-time, there still don't exist global inertial coordinate systems for curved space-times.