A mirror behind the event horizon

Thought experiment:

What will happen if you place a mirror behind the event horizon and turn on the light in its direction?

What do you mean by ”place”? It cannot remain stationary there.

Bosko said:

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Let me also add that the above depiction is quite misleading. It is not an accurate depiction of the Schwarzschild spacetime. The singularity is not like a place in space but more like a moment in the future. A more accurate depiction would be using something like a Kruskal diagram to show what you actually mean.

Edit: Bottom line is, you have to start thinking about spacetime as a whole. Not just like space with time tucked on as an afterthought. Particularly in environments so extreme as a black hole.

The mirror falls into the singularity. Light may bounce off it while it is falling (if you turned the lamp on quick enough), but the reflected light will also fall into the singularity. As @Orodruin says, your diagram badly misrepresents the structure of the interior, which may make what I said seem implausible. The problem is with your diagram. A Kruskal diagram will allow you to illustrate the situation well enough to see what's going on.

Did you ask yourself what happens if you plave a lightbulb behind the event horizon? If not, why not? If so, why is reflecting light from a mirror any different than just turning on the light?

Orodruin said:

Let me also add that the above depiction is quite misleading. It is not an accurate depiction of the Schwarzschild spacetime. The singularity is not like a place in space but more like a moment in the future. A more accurate depiction would be using something like a Kruskal diagram to show what you actually mean.

I want to hear other people's opinions, to better understand ...
How the two singularities (0,Rs) appeared in the Schwarzschild solution
To better understand the Kruskal coordinates that remove the Rs singularity
...

Orodruin said:

Edit: Bottom line is, you have to start thinking about spacetime as a whole. Not just like space with time tucked on as an afterthought. Particularly in environments so extreme as a black hole.

I'm just trying to figure it out.
Anything that, in my mind, I try to put beyond the event horizon ceases to exist :-)
The light cone no longer makes sense...

Vanadium 50 said:

Did you ask yourself what happens if you plave a lightbulb behind the event horizon? If not, why not? If so, why is reflecting light from a mirror any different than just turning on the light?

I would like to hear what people think happens when light or some physical object goes towards the event horizon.
Perhaps their opinion on the information paradox of the black hole ...
To hear their opinion, think about it and possibly improve my own.

Bosko said:

How the two singularities (0,Rs) appeared in the Schwarzschild solution

Incorrect. The singularity at r = Rs is not an actual singularity, but rather due to a bad choice of coordinates.

Bosko said:

To better understand the Kruskal coordinates that remove the Rs singularity

It was never there. Just a bad choice of coordinates. Like trying to use polar coordinates at the origin in Euclidean space.

Bosko said:

The light cone no longer makes sense...

It does make perfect sense. If you still use Schwarzschild coordinates, it is just that the negative r direction is the future timelike one.

You can also look at a Kruskal diagram …

Bosko said:

Perhaps their opinion on the information paradox of the black hole ...
To hear their opinion, think about it and possibly improve my own.

Before you start thinking of anything like that you should make sure that you have a solid grasp of the actual classical GR solutions and what happens there.

Bosko said:

I would like to hear what people think happens when light or some physical object goes towards the event horizon.

Mathematics is not opinion. "Chunky peanut butter is better than smooth peanut butter" is an opinion.

Orodruin said:

Incorrect. The singularity at r = Rs is not an actual singularity, but rather due to a bad choice of coordinates.

In the mathematics of the original Schwarzschild solution, there was another singularity, otherwise I don't see the motivation for introducing the Kruskal diagram.

Orodruin said:

It was never there. Just a bad choice of coordinates. Like trying to use polar coordinates at the origin in Euclidean space.

You mean that mathematical model did not represent something physically real

Orodruin said:

It does make perfect sense. If you still use Schwarzschild coordinates, it is just that the negative r direction is the future timelike one.

Everything is only moving straight towards the future singularity.

Orodruin said:

You can also look at a Kruskal diagram …

Before you start thinking of anything like that you should make sure that you have a solid grasp of the actual classical GR solutions and what happens there.

All right. The mathematical model is mostly clear to me, but not its physical meaning

Vanadium 50 said:

Mathematics is not opinion. "Chunky peanut butter is better than smooth peanut butter" is an opinion.

Mathematics makes models. Perhaps some do not represent reality well.
It may happen that in some situations a small plastic car (model) does not describe well the behavior of a real car.
I want to hear that opinion about the mathematical model.

Schwarzschild coordinates use the timelike Killing vector field as their timelike basis vector and its spacelike basis vectors are orthogonal to it. Unfortunately the "timelike Killing field" is null on the horizon so this process fails. This was, of course, not obvious to Schwarzschild.

Alternatively, you can argue that Schwarzschild spatial planes are defined consistent with the radar method. If I emit a radar pulse at time ##t_e## and receive a reflection at ##t_r## then the event it reflected off was at time ##(t_e+t_r)/2##. This process goes wrong at the event horizon because the reflection never returns. Again, this wouldn't have been obvious to Schwarzschild.

Bosko said:

I want to hear other people's opinions, to better understand ...

Physics is not about opinions. If you want to better understand what a physical theory predicts in a particular scenario, you need to learn how the theory works, i.e., the mathematical model it uses and how quantities in the model correspond to quantities you actually measure. We can certainly help you with that here, but it won't be by giving you our opinions.

Bosko said:

I want to hear that opinion about the mathematical model.

No, you don't. If this thread belongs in this forum at all, then you want to learn how the mathematical model works. That is not a matter of anyone's opinion.

Bosko said:

In the mathematics of the original Schwarzschild solution, there was another singularity

I'm not sure what you mean. Schwarzschild himself never discovered the true curvature singularity at what we now call ##r = 0##. The coordinates he was using only covered the region outside the horizon, which made it look to him like the horizon, what we now call ##r = 2M##, was a singularity. But he was wrong: it isn't.

Bosko said:

I don't see the motivation for introducing the Kruskal diagram.

The Kruskal diagram is based on a coordinate chart that covers the entire maximally extended manifold of Schwarzschild spacetime. No other chart known at the time did so. That's why it was introduced.

Bosko said:

You mean that mathematical model did not represent something physically real

No, he means that mathematical model only represented a portion of the spacetime, the portion outside the horizon (and only one of the two such portions in the Kruskal diagram at that, the right wedge, usually called region I).

Bosko said:

Everything is only moving straight towards the future singularity.

Inside the horizon this is more or less true (my only reservation is what you mean by the word "straight"; but you can leave that word out and the statement will be true).

Bosko said:

The mathematical model is mostly clear to me, but not its physical meaning

What's unclear about the physical meaning? The key point is that your scenario is physically impossible because no object can remain stationary at or inside the horizon. What's unclear about that?

Bosko said:

How the two singularities (0,Rs) appeared in the Schwarzschild solution...
In the mathematics of the original Schwarzschild solution, there was another singularity,

There is only one singularity in the Schwarzschild solution, the one at ##r=0## (be aware that describing the singularity that way is mathematically sloppy, it's a "you know what I mean" handwave).

There are two singularities in Schwarzschild coordinates, one at ##r=R_S## and one at ##r=0##. The one at ##R_S## is an artifact of this particular coordinate choice; it's just the math telling us that we can't use these coordinates at the event horizon, for about the same reason that we can't use longitude at the north pole (even though there is nothing singular or different about the surface of the earth there).

Nugatory said:

There is only one singularity in the Schwarzschild solution.

Actually, there are two in the maximally extended solution (the Kruskal diagram). I think that's worth noting since the OP has asked about that diagram.

Bosko said:

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Your diagram here is wrong. The singularity is not a point in space. It's a moment of time.

PeterDonis said:

Actually, there are two in the maximally extended solution (the Kruskal diagram). I think that's worth noting since the OP has asked about that diagram.

Ah - yes there are. I was rolling all the way back to the original post.

Vanadium 50 said:

Mathematics is not opinion. "Chunky peanut butter is better than smooth peanut butter" is an opinion.

That chunky peanut butter is better than smooth peanut butter has been mathematically proven, I believe.