Can things move faster than light inside the event horizon of a black hole?

Question

Black Holes are regions of space where things get weird ^{[Citation Needed]}. Past the event horizon of a black hole, any moving particle instantaneously experiences a gravitational acceleration towards the black hole that will cancel out it's current velocity, even light. That means that the gravity well of the black hole must be able to accelerate from -C¹ to 0 instantly². Given that fact, we can assume the gravitational acceleration of black holes is C/instant³. Given this, it stands to reason that in successive instants, the particle will be moving at speeds greater than C, because it is experiencing greater gravitational forces and continuous gravitational acceleration.

Does this actually make sense? Is there something I'm missing here? By this logic, it seems like anything inside of the event horizon of a black hole could and should move faster than C due to gravitational acceleration.

Edit: I showed this question to a friend and he questioned if the hypothetical particles that were radiating from the singularity (The photon traveling exactly away from the black hole) might be hawking radiation; that is, the gravitation acceleration of a black hole is only strong enough to curve the path of light around a non-zero radius (thus not actually stopping it, but altering it's course), and not powerful enough to decelerate light. Is this actually what hawking radiation is, or is he as confused as I am?

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¹ Where movement towards the singularity would be considered a positive value, movement away from the singularity is a negative value, that is, anything moving at the speed of light away from the singularity would be moving with a velocity of -C relative to the singularity.

² If it couldn't accelerate from -C to 0 instantly, any photon traveling exactly away from the black hole would be able to escape the event horizon.

³ An instant is an arbitrary amount of time, it could be a fraction of a second, a second, a minute....

Answer 1

I think your initial question is a good one, but the text gets a bit more jumbled and covers a few different points.

Can things move faster than light inside the event horizon of a black hole?

Nice question.

Black Holes are regions of space where things get weird.

I'm 100% OK with this statement. I think it's a true enough summary and I'm sure I've heard physicists say this too. Even if "Weird" isn't a clearly defined scientific term, I'm 100% fine with this (even without a citation).

Past the event horizon of a black hole, any moving particle instantaneously experiences a gravitational acceleration towards the black hole that will cancel out it's current velocity, even light. That means that the gravity well of the black hole must be able to accelerate from -C* to 0 instantly✝.

Are you quoting somebody here? Anyway, this isn't quite true. Black holes don't accelerate things from -c (which I'm guessing would be a light beam trying to fly away from the singularity but inside the event horizon), to 0 "instantaneously".

Perhaps a better way to look at it is to consider curvature of space, and inside a black hole, space curves so much that all directions point to the singularity. It's the "all roads go to Rome" scenario, even if you do a complete 180, you're still on a road that leads to the singularity.

I understand the temptation to look at that as deceleration, but I think that's a bad way to think about it. Light doesn't decelerate, it follows the curvature of space.

Given that fact, we can assume the gravitational acceleration of black holes is C/instant**. Given this, it stands to reason that in successive instants, the particle will be moving at speeds greater than C, because it is experiencing greater gravitational forces and continuous gravitational acceleration. Does this actually make sense? Is there something I'm missing here? By this logic, it seems like anything inside of the event horizon of a black hole could and should move faster than C due to gravitational acceleration.

outside of a black hole, continuous acceleration would never lead to a speed greater than C. You can accelerate for billions and trillions of years and all you'd do is just add more 9s to the right of the decimal point.

You seem to be assuming that inside a black hole this can happen, but I'm not sure why you'd assume that.

"continuous gravitational acceleration" - no matter how strong, is no guarantee for faster than light travel. That's logically inconsistent with the laws of relativity.

Edit: I showed this question to a friend and he questioned if the hypothetical particles that were radiating from the singularity (The photon traveling exactly away from the black hole) might be hawking radiation; that is, the gravitation acceleration of a black hole is only strong enough to curve the path of light around a non-zero radius (thus not actually stopping it, but altering it's course), and not powerful enough to decelerate light. Is this actually what hawking radiation is, or is he as confused as I am?

I think, a more correct way to look at hawking radiation is to see it as something that forms just outside of the black hole, a particle/anti particle pair and one escapes and the other falls inside, and that's probably not 100% correct either, but the singularity itself doesn't send out particles. Hawking radiation has to do with quantum properties of space. It's not a property of black holes. The black hole just happens to be unique in that it can capture one half of a virtual particle pair and the other half can escape.

This also is a pretty different topic than your original question.

*Where movement towards the singularity would be considered a positive value, movement away from the singularity is a negative value, that is, anything moving at the speed of light away from the singularity would be moving with a velocity of -C relative to the singularity. ✝If it couldn't accelerate from -C to 0 instantly, any photon traveling exactly away from the black hole would be able to escape the event horizon.

**An instant is an arbitrary amount of time, it could be a fraction of a second, a second, a minute....

I think it's a good idea to differentiate mass-less pure energy particles and particles with mass. You seem to be saying that a ray of light can be traveling away from a black hole at the speed of light, get caught in the gravity, slow down and then fall back into the black hole like a ball that's tossed straight up into the air from the surface of the Earth. That's probably not what happens. The ray of light follows the path of space time ahead of it, which happens to be curved so much that it points into the black hole, even if, in the classical sense, the light begins by pointing away. All space curves into the singularity once you're inside the event horizon, so there is no "away from" anymore. At least, that's how I think it works.

Answer 2

The short answer to your top-level question "Can things move faster than light inside the event horizon of a black hole?" is no. The text of your question gets confusing and contains a lot of assumptions that are not correct. There's no "special" acceleration happening at or near the event horizon. If things could travel faster than the speed of light there, then they would potentially be able to escape the black hole. The hole is "black" because things are bounded by the speed of light and because of the spacetime curvature.

Answer 3

Can things move faster than light inside the event horizon of a black hole?

We don't know. We do not have any accepted, verifiable–or even more essential: falsifiable–theory about the inside of an event horizon. And this is not because our apparatuses aren't powerful enough (yet), it's of a fundamental nature. If something doesn't emit anything, how could we be able to detect anything?

It is, however, not very likely since „It is generally assumed that fundamental constants such as c have the same value throughout spacetime, meaning that they do not depend on location and do not vary with time.“.

OK, there's the Hawking radiation but that's emitted close to the surface of the event horizon (on the outside).

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BTW, things can move faster than light on the moon. If you hold a laser in your hand that's strong enough to create a light spot on the moon and if you turn your hand fast enough (with more than 0.76–0.82 Hz, i.e. about a quarter of a revolution in a third of a second–that's easy to do [select Unit conversion: more there, then scroll down]) the light spot moves faster than $ c $.

PLEASE NOTE: There's no transfer of mass, energy or information involved in a laser beam projection point movement! So, Newton, Huygens, Rømer, Bradley, Fizeau, Foucault, Newcomb, Arago, Fresnel, Michelson & Morley and Einstein, amongst many others, are still right.

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Past the event horizon of a black hole, any moving particle instantaneously experiences a gravitational acceleration towards the black hole ...

Not only past the event horizon. In fact, everywhere in the rest of the universe. Remember, gravity cannot be shielded and has unlimited reach. So it's not instantaneously as soon as it passes the event horizon, it's already long before. (BTW, instantaneous, i.e. with zero $ \Delta t $, in conjunction with speed leads to terms like $ \frac {\Delta s} 0 $. Mathematicians–and also physicists–don't like such too much.)

... that will cancel out it's current velocity, even light.

Cancel out to zero? No. It's more that the mass of the black hole bends space so hard that particles (or light) stay inside the event horizon while still moving along geodesics, which are straight lines in the Euclidean space we know from everyday experience, but aren't straight at all near (big) masses; see Eddington experiment and gravitational lens.

That means that the gravity well of the black hole must be able to accelerate from -C¹ to 0 instantly².

No, it doesn't have to. (Note: A decrease of the magnitude [or length] of a velocity vector is usually called deceleration.)

Given that fact, we can assume the gravitational acceleration of black holes is C/instant³.

No, we can't assume that. We can rely on Newton's law of universal gravitation

$$ F = G \frac {m_1 m_2}{r^2} $$

where the force for

$$ a = \frac F m $$

decreases with the square of the distance and such the acceleration decreases equally. Closer to the black hole we will have to use Einstein's equations of his GTR.

Answer 4

As is often the case in GR, it depends on who is measuring and what exactly they are measuring, but basically the answer is no.

How do you measure a speed? You take your watch and you see how long it takes you to travel between two fixed points with a known distance between them. Alternatively you could get somebody at a fixed position to measure your speed with a radar gun as you zoom past.

Neither of these options is available inside the event horizon of a black hole. There are no fixed points. You cannot erect stationary mileposts because everything must move inwards. In fact, the proper distance between any two radial coordinates inside the event horizon is imaginary (i.e. the square root of a negative number) - which is telling you that it is not possible to measure the distance between the coordinates using a measuring stick. Neither is it possible for someone to measure your speed with a radar gun for the same reason - there can be no observer at some fixed radial point to measure your speed.

Why then am I confident that you travel slower than light? Because what you can do is try and race an ingoing light pulse to the singularity. It is easy to show that, starting from any radial coordinate and using any kind of time coordinate, the light always gets there first - therefore you do not travel faster than the speed of light.

There are numerous items in the question that are not in accord with General Relativistic thinking. Gravity is not a force in GR. A falling body does not experience an acceleration it simply follows the path that maximises its proper time between two events. That is not to say that $d^2r/dt^2 = 0$ (it isn't), but nobody measures $r$ or $t$ and saying $dr/dt>c$ inside the event horizon is as meaningful as pointing out that if you go fast enough then you can travel to the nearest stars in minutes as measured on your own watch, but nobody would ever say your speed was $>c$. Light too is not accelerated. It is always measured to be travelling at $c$ when measured in any local inertial frame.

Answer 5

Suppose an object is falling into a black hole. As the object passes the event horizon, it must be traveling at the speed of light, because if you reverse the path it will just barely make it out of the black hole if traveling the speed of light. So beyond the event horizon, it is natural to think that the speed must be greater. Normally you can’t push something faster than c because its mass increases, but gravitational acceleration is independent of mass, so why doesn’t it continue to accelerate? Somehow though the mass is prevented from accelerating any further even though it is in a gravitational field. You have to go to the picture where all objects travel through spacetime at the speed of light, and the gravitational force we experience is just an artifact of the shape of spacetime, there is no real acceleration going on in our travel through spacetime, it is always at the speed of light. Inside the black hole the speed is still the same but the spacetime is warped so much that our usual concepts of space and time do not apply anymore. There is no “up”, only “down”, and time flows both forward and backwards. So we get into trouble if we try to apply our common-sense notions of speed and acceleration.