Can a Black Hole's Event Horizon Ever Collapse in on Itself?

[peteb]

I saw this question posted in a Yahoo forum. I would be interested in the answers from the people here:

"We can all agree that the more massive a black hole is the smaller the circumference of the black hole's event horizon will be. Therefore, can a black hole ever have enough mass to where its event horizon closes in on itself? If so, what would happen?

I think that if all of time/space, mass and energy coalesced in a singularity, there would have to be a type of explosion where the inverse would be everything will be expanding." Posted by Steve B.


Pete B

 

[nicksauce]

I don't agrere with the premise. The radius of the horizon is given by R = 2GM, so if M increases then the radius of the horizon increases. Secondly, the event horizon is a 2 dimensional sphere, so how are you defining its circumference?

 

[Chronos]

The source you appear to be quoting makes fantastic, unsupported, and unreliable claims. Aside from that, it looks reliable.

 

[peteb]

I think Steve was correct in what he said:

"We can all agree that the more massive a black hole is the smaller the circumference of the black hole's event horizon will be. Therefore, can a black hole ever have enough mass to where its event horizon closes in on itself? If so, what would happen?

I think that if all of time/space, mass and energy coalesced in a singularity, there would have to be a type of explosion where the inverse would be everything will be expanding.".


It seeems to me, the event horizon of a black hole is the horizon, viewed from inside the black hole, where the escape velocity of a light beam is greater than the speed of light, and thus is the horizon where all lght escaping from the hole would be bent back into the hole. The more massive the black hole, the smaller (in radius inside the black hole) that event horizon would be. A supermassive black hole, say containing ten thousand stellar masses, would have a vastly smaller event horizon **inside the black hole** than a black hole containing say one stellar mass at its core; but the actual supermassive black hole itself would be the same size as any other black hole.

The Schwarzschild radius concerns masses and observers and phenomena outside of a black hole, not mass within a black hole, it relates how much mass is required to generate a black hole. Once the black hole forms, though, it can suck in mass from beyond its event horizon, which will cause the event horizon to decrease in diameter inside the black hole (IOW a light beam or an atomic particle generated inside the black hole will be turned back into the hole, unable to escape, at distances much closer to the the singularity at the center of the black hole because the gravitational force acting on that light beam, attributable to the gravity of that mass inside the black hole, will be stronger in proportion the mass within that singularity at the center.



http://en.wikipedia.org/wiki/Event_horizon

"In general relativity, an event horizon is a boundary in spacetime, most often an area surrounding a black hole, beyond which events cannot affect an outside observer. Light emitted from beyond the horizon can never reach the observer, and any object that approaches the horizon from the observer's side appears to slow down and never quite pass through the horizon, with its image becoming more and more redshifted as time elapses. The traveling object, however, experiences no strange effects and does, in fact, pass through the horizon in a finite amount of proper time."

...

"...The most commonly known example of an event horizon is defined around general relativity's description of a black hole, a celestial object so dense that no matter or radiation can escape its gravitational field. This is sometimes described as the boundary within which the black hole's escape velocity is greater than the speed of light. A more accurate description is that within this horizon, all lightlike paths (paths that light could take), and hence all paths in the forward light cones of particles within the horizon, are warped so as to fall farther into the hole. Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time (and can actually be thought of as equivalent to doing so, depending on the spacetime coordinate system used). ..."


Pete B

 

[George Jones]

I think Steve was correct in what he said:

"We can all agree that the more massive a black hole is the smaller the circumference of the black hole's event horizon will be. Therefore, can a black hole ever have enough mass to where its event horizon closes in on itself? If so, what would happen?

I think that if all of time/space, mass and energy coalesced in a singularity, there would have to be a type of explosion where the inverse would be everything will be expanding.".

This is quite wrong. For uncharged, spherical black holes, the correct answer has been given by nicksauce in post#2.

 

[peteb]

OK then, George, are you saying that, contrary to what the Wiki article states, as the mass inside the black hole increases, a light beam coming from the inside of that black hole traveling out toward the event horizon will travel **farther out** from the center before it bends back into the black hole? That is not what the Wiki article seems to say, so are you saying the article is incorrect?

Pete B

 

[Chronos]

The event horizon increases with mass. This is pretty basic, and akin to the premise the gravitational influence of the sun extends to greater distance than that of earth. The event horizon is the distance at which escape velocity = c and it increases with mass. Perhaps you misunderstood the article.

 

[George Jones]

OK then, George, are you saying that, contrary to what the Wiki article states, as the mass inside the black hole increases, a light beam coming from the inside of that black hole traveling out toward the event horizon will travel **farther out** from the center before it bends back into the black hole?

It took me a while, but I now think that I might understand what you're getting at.

First an analogy. Suppose that I stand on the Earth and throw a baseball straight up with speed v. The baseball reaches a maximum height H before turning around and coming back down. Now suppose that the Earth is the same size, but is now made of a denser material (e.g., gold), so that the Earth is now more massive. Again, I throw a base ball up with the same speed v. Now, however, the baseball reaches a h with h < H. The two baseballs started at the same distance from the Earth's centre.

Now redo this starting inside black holes with photons instead of baseballs. Is this what you mean? I think the problem lies with your interpretation of the eventg horizon. The event horizon is not the "maximum height" reached by photons fired "straight up".

Suppose you decide to plunge straight into a black hole. Suppose further that during your entire trip, both inside and outside the black hole, there is a particular star that you can see directy behind (i.e., directly above) you. At some time inside the horizon, you briefly fire two lasers simultaneously, one in the direction of star (straight up), and one in a direction opposite to the star (straight down). As expected, the light from the laser fired straight down immediately heads away from the event horizon. But, maybe unexpectedly, the light from the laser fired straight up also immediately heads straight down relative to the event horizon! (Technical note: this works because, for Schwarzschild black holes, the apparent and event horizons coincide.)

For a diagram of the "motion" of you and the light from the two lasers, see FIFURE 9 on page 25 of

http://www.eftaylor.com/exploringblackholes/InsideBH091104v3.pdf .

Note how even the outgoing (straight up) light bends away from the event horizon and towards the singularity.

 

[peteb]

OK I agree with those who say the original statements I quoted were incorrect. I never really thought they were right, but I was not sure of the explanation for the error. All settled.

Pete B