How can light be trapped in a black hole?

[Jur van Oerle]

I have learned that light has a constant speed of 299 792 458 m / s or C and that this speed cannot be changed by anything, how can a black hole "trap" light if this speed cannot change?
Is it because time is also trapped, so a second lasts infinitely long?

 

[mfb]

Once you are inside a black hole, every "direction" is towards the center. There is simply no direction that would be "outwards".
Note the " " as those concepts are not very meaningful in a spacetime that is so extremely curved as in a black hole.

 

[Jur van Oerle]

Hi @mfb ,
thank you for your reply. I still don't fully understand; do you mean that light will orbit the center of the black hole?

 

[CentrifugalKing]

Once anything is in a black hole, it is trapped there. Black Hole's gravitational forces are way too strong. And to the outside observer we can see anything.

 

[Jur van Oerle]

Hi @CentrifugalKing,
Thank you for your reply, however I know that happens inside a black hole but that wasn't my question.
My question in: If light always travels at the speed of light regardless of circumstances, how can it be trapped?
In other words: how can the speed of light be changed if it is physically impossible to travel less than the speed of light?

 

[A.T.]

If light always travels at the speed of light...

Only in a local free falling frame, not in non-inertial coordinates.

 

[CentrifugalKing]

Light travels in a straight light. Under heavy gravitational forces, light will curve. Black holes bend spacetime. So no matter what path the light goes, it'll bend back at the center.

 

[Jur van Oerle]

Only in a local free falling frame, not in non-inertial coordinates.

I don't know what any of these words mean :P

 

[CentrifugalKing]

Non-inertial reference frames are reference frames that are accelerating.

 

[Jur van Oerle]

Light travels in a straight light. Under heavy gravitational forces, light will curve. Black holes bend spacetime. So no matter what path the light goes, it'll bend back at the center.

I think I understand better now, light does not travel slower but instead, the distance it has to travel is infinite because the space around the light particle is curved.
I's still a bit lost thought but I guess it takes more than a few lines of information to fully comprehend these kinds of things.
Thank you for your time :)

 

[mfb]

Hi @mfb ,
thank you for your reply. I still don't fully understand; do you mean that light will orbit the center of the black hole?

No, it will hit the center. Every direction, every possible velocity and acceleration leads to the center, it is impossible to avoid hitting it.

There is simply no way that would go from the inside to the outside.

 

[phinds]

Right at the Event Horizon, if any light were generated by a photon-producing process, the resultant photon, if headed away from the singularity, can be traveling outward at c as measured locally, but as has been said, spacetime is "bent" in gravitational fields and it happens that at the Event Horizon (because of the definition of the Event Horizon) the bending is exactly equivalent to c so from the reference point of observer outside the BH, that light "appears" (actually it would be more correct to say "is calculated as being" since you can't really see it) stationary at the EH.

At every point inside the EH, the light follows the local geodesic back to the center of the BH so light at the EH cannot have been created inside the EH because such light can never reach the EH. It cannot be generated outside the EH because such light will be traveling inward when it reaches the EH and thus will inevitably travel further inward to the singularity.

I think there are more complex situations and @mfb I would appreciate your comments on what I have just said.

 

[Jur van Oerle]

Right at the Event Horizon, if any light were generated by a photon-producing process, the resultant photon, if headed away from the singularity, can be traveling outward at c as measured locally, but as has been said, spacetime is "bent" in gravitational fields and it happens that at the Event Horizon (because of the definition of the Event Horizon) the bending is exactly equivalent to c so from the reference point of observer outside the BH, that light "appears" (actually it would be more correct to say "is calculated as being" since you can't really see it) stationary at the EH.

At every point inside the EH, the light follows the local geodesic back to the center of the BH so light at the EH cannot have been created inside the EH because such light can never reach the EH. It cannot be generated outside the EH because such light will be traveling inward when it reaches the EH and thus will inevitably travel further inward to the singularity.

I think there are more complex situations and @mfb I would appreciate your comments on what I have just said.

Thanks.
This is the most detailed response to my question and I think I understand it and the answer to it better. Some thing are still vague though, like what you mean by bending space-time and why that is any different from throwing a ball and watch it fall down to Earth (or any other object exerting enough gravity).

 

[phinds]

Thanks.
This is the most detailed response to my question and I think I understand it and the answer to it better. Some thing are still vague though, like what you mean by bending space-time and why that is any different from throwing a ball and watch it fall down to Earth (or any other object exerting enough gravity).

"bending" is a very poor description of what is going on. It is a term that we use because we humans have evolved in a world that is to all of our senses classical rather than quantum or cosmological, and we have an innate bias towards Euclidean geometry since that was how we survived. Believing, for example, that one could throw a spear at some animal you hope to eat and expect the spear to follow a Riemann geometry path (even assuming cavemen knew what Riemann geometry was, which they did not) would lead to starvation.

Space-time, on the other hand, follows Riemann geometry, not Euclidean, and thus straight lines (more properly "geodesics") appear curved or bent when viewed from the perspective of Euclidean geometry.

So we SAY it is "bent" but in its own framework it really isn't.

 

[Dale]

how can a black hole "trap" light if this speed cannot change?

The event horizon is a null surface, meaning that locally it is moving at the speed of light. If you flash two pulses of light from some emitter then the surface defined by the first flash also "traps" the light from the second flash, even in flat spacetime. Also, even in flat spacetime if you accelerate constantly in some direction then there will be light pulses that are "trapped" in the sense that they cannot ever reach you.

 

[PeterDonis]

how can a black hole "trap" light if this speed cannot change?

The trapping doesn't involve changing the speed of light; it involves changing what directions in spacetime it can travel. Inside a black hole's horizon, every null direction (i.e., every direction a light ray's worldline can go in spacetime) ends up leading to the singularity. Light travels along any such worldline at the speed of light; but because all the worldlines end up at the singularity, that's where the light ends up.