# Blackhole Question (involves Light)

lifeisareaction
Help me out. I understand that the speed of light is thought of as the maximum speed in the universe. However, if the gravity of a black hole can suck in light, wouldn't that mean that the gravity of a black hole could accelerate matter until it surpassed the speed of light?

No. When you accelerate something near the speed of light, most of the energy goes into increased mass, not into speed. Particle accelerators must take this into account for them to work properly.
The effect of black holes is based on the fact that the escape velocity is greater than the speed of light.

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Welcome to Physics Forums, lifeisareaction!

Staff Emeritus
In order to measure the speed of something falling into a black hole, you need a reference frame.

If you adopt a reference frame of a "stationary observer" who is hovering at some distance 'r' away from the black hole, it turns out that the speed of any matter falling into the black hole approaches 'c' as r approaches the Schwarzschild radius. One could losely describe this state of affairs as an object reaching the speed of light at the event horizon - after which it continues to accelerate.

However, stationary observers do not exist exactly at the event horizon, or anywhere inside it. Inside the event horizon, all observers are falling into the black hole.

So there is no actual observer who ever sees the infalling matter exceed or even reach 'c'. But it is possible for the rate of change of the Schwarzschild 'r' coordinate with respect to the Schwarzschild 't' coordinate to exceed the speed of light, in fact it turns out that one expects this to happen inside the event horizon. However, that this is a 'coordinate velocity" that no physical observer will ever observe. One might think of this as the velocity that a stationary observer inside the event horizon would measure, if a stationary observer could exist. (But of course, such an observer cannot exist!).

There is some mathematical background on a very closely related question at

https://www.physicsforums.com/showpost.php?p=602558&postcount=29
https://www.physicsforums.com/showpost.php?p=621784&postcount=31

(the first post in mine, the second is another poster, George Jones).

If you adopt a reference frame of a "stationary observer" who is hovering at some distance 'r' away from the black hole, it turns out that the speed of any matter falling into the black hole approaches 'c' as r approaches the Schwarzschild radius.

It is my impression that, to an outside observer, the object falling into a black hole appears to slow down to a crawl, never actually reaching the event horizon.

kublai
mathman said:
It is my impression that, to an outside observer, the object falling into a black hole appears to slow down to a crawl, never actually reaching the event horizon.

hmmm, if that were true how did that black hole get all that matter to make a black hole? If the event horizon was laden with objects that never reached inside it would not be black, would it?

My statement refers to the frame of the outside observer. In the reference frame of the falling object or of the black hole, the object just falls in. When you see descriptions of black holes being formed from collapsing stars (see Kip Thorne's Black Holes and Time Warps), the star never appears to the outside observer to make it to the black hole stage. The light from the star just keeps getting redder.

Staff Emeritus
mathman said:
It is my impression that, to an outside observer, the object falling into a black hole appears to slow down to a crawl, never actually reaching the event horizon.

To the outside observer at r=infinity, the object falling into the black hole appears to slow down to a speed of zero.

To the outside obsever, stationary with respect to the black hole, the object falling into the black hole approaches a velocity of 'c' as the stationary observer and the object, both assumed to be at the same point in space, approach r=R_s, the radius of the event horizion of the black hole.

For the details, see the links to the previous thread I posted.

As I mentioned before, it requires infinite acceleration to "hover" at the event horion of a black hole, so the velocity of c is never measured, only approached as a limit.