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Andrew D
2010-Feb-14, 01:33 AM

1. What do we know about the behavior of light inside of the EH of a BH?

1a. Imagine the flashlight falling toward the EH from outside of it, shining a beam of light tangent to the EH. What I assume is that the light beam would bend more and more as the flashlight approached, at the EH the light would bend along the EH, and below the EH the light would bend enough to 'shine' down toward the singularity. Is this correct?

1b. Obviously, gravity bends photons like it does any other particle (i.e. gravitational lensing). So would photons from a flashlight shined from the interior of the EH toward the outside 'bend' back to the center, or just become red-shifted 'infinitely' and never 'escape', but maintain the same path? (My intuition tells me the first is true for photons with angular momentum, but the second is true for photons traveling against the gradient)

1c. If it is important whether or not the photons are traveling perpendicular to the gravity gradient (away from the singularity), then what is the difference in behavior between photons travelling perpendicularly and those with angular momentum?

2. What would an observer see inside the EH (lets assume the EH was a sufficient distance away from the singularity that an observer had time to actually observe)?

2a. Wouldn't the direction away from the singularity appear extremely blue-shifted, and become more blue-shifted as the observer got closer to the singularity?

2b. Wouldn't the direction toward the singularity appear just as red-shifted as the EH appears to an outside observer?

2c. Following that logic, wouldn't space within the radius of the observer appear (to the observer) as though it was the EH, such that the observer would see himself embedded in a black horizon, extreme darkness (red-shifted) in front of him, and a blue-shifting universe behind him?

3. What exactly is the difference between 'velocity induced' time dilation and gravitational time dilation? As an object has more mass the faster it travels, are they the same effect, in that the increased gravitational field of the object is causing the time dilation? Or, conversely, is the increasing time dilation of an object responsible for its increase in mass ( i.e. charge over wire = magnetic field, and magnetic field over wire = charge)?

I assure you I'm asking out of curiosity and an eagerness to understand, and I'm not cooking up and crazy ATM ideas.

Also, If any questions require parameters that I have not specified, I apologize. Just assume the obvious, show an example from one perspective, or tell me what you need, etc.

astromark
2010-Feb-14, 06:21 AM
Most of your questions are evidence enough that you have a already good understanding of what a black hole is.
It is not an empty space where light rattles around not being able to escape.
Astronomicle science has proven that a black hole is...real.
Because of the massive amount of matter condensed into a very small space the fabric of mater as we would recognize it has no space to be... the fact that this massive gravity well of extrema tempreture and denseness... prohibits lights escaping it. The photon stream from your torch would never reach the observer outside the BH. But the torch would never have made it without being ripped asunder first. This question and all of the related questions that normally follow.. are not new here. A little Search.. will find you much much more than I can hope to expound...:)he, he, he.

Andrew D
2010-Feb-14, 12:07 PM
Thanks. I think I pretty much answered my questions to myself while thinking how to ask them, but I figured I'd confirm that my conclusions were correct.

Tensor
2010-Feb-14, 02:15 PM
You got a lot of the answers yourself, but there are one or two points that need clarification, so

1. What do we know about the behavior of light inside of the EH of a BH?

It becomes a bit complicated inside the EH as lightlike paths become timelike and timelike paths become lightlike. (if you need a explanation for those try here ( http://en.wikipedia.org/wiki/Spacetime) .

1a. Imagine the flashlight falling toward the EH from outside of it, shining a beam of light tangent to the EH. What I assume is that the light beam would bend more and more as the flashlight approached, at the EH the light would bend along the EH, and below the EH the light would bend enough to 'shine' down toward the singularity. Is this correct?

Again, the paths become complicated, but basically, you got it right.

1b. Obviously, gravity bends photons like it does any other particle (i.e. gravitational lensing). So would photons from a flashlight shined from the interior of the EH toward the outside 'bend' back to the center, or just become red-shifted 'infinitely' and never 'escape', but maintain the same path? (My intuition tells me the first is true for photons with angular momentum, but the second is true for photons traveling against the gradient)

Not sure what you mean by the same path (I'm thinking you mean a path straight out of a black hole ie. at a 90 degree angle to the event horizon.). All paths are curved inside a black hole, so all photons would bend back toward the singularity.

1c. If it is important whether or not the photons are traveling perpendicular to the gravity gradient (away from the singularity), then what is the difference in behavior between photons travelling perpendicularly and those with angular momentum?

None to speak of, other than following a different path to the singularity.

2. What would an observer see inside the EH (lets assume the EH was a sufficient distance away from the singularity that an observer had time to

snip...

extreme darkness (red-shifted) in front of him, and a blue-shifting universe behind him?

For purposes of a simplified outlook, you got it pretty much right in your questions 2a,2b,2c.

3. What exactly is the difference between 'velocity induced' time dilation and gravitational time dilation?

None, except for the cause.

As an object has more mass the faster it travels, are they the same effect, in that the increased gravitational field of the object is causing the time dilation?

Ok, be very careful here. Mass does not increase as velocity increases. In the language of four-vectors (the math used in SR), mass is an invariant. The momentum four vector has four terms, three momentum and one mass. That mass term never changes, but the momentum terms do. The total magnitude of the vector does change as a result. The magnitude indicates the total energy of the object in question.

Or, conversely, is the increasing time dilation of an object responsible for its increase in mass ( i.e. charge over wire = magnetic field, and magnetic field over wire = charge)?

While the equations between EM and gravity look similar, there are subtle differences in the way the equations of gravity works. In this case, no, the increasing time dilation has no effect on the increase in mass.

I assure you I'm asking out of curiosity and an eagerness to understand, and I'm not cooking up and crazy ATM ideas.

No problem. They look pretty much like straight up questions to me. If are really interested and you are not mathematically inclined, I would highly recommend you find Kip Thorne's book "Black Holes and Time Warps: Einstein's Outrageous Legacy" It does a very good job of explaining black hole (along with some very good history of those involved with the theoretical discoveries), both inside and outside the EH.

Andrew D
2010-Feb-14, 02:38 PM
Thanks tensor, thats really helpful. I just read Susskind's Black Hole War, and was directed then to read his An Introduction To Black Holes, Information And The String Theory Revolution: The Holographic Universe, though the math is way past where i'm at right now. I'm actually studying mathematics at university, but I'm only in my second year, so ... in time...

again, thanks so much.

Andrew D
2010-Feb-14, 08:21 PM
Update: I just bought an old copy of Black Holes and time-warps for \$2.65. Thanks.

I'm always interested in books to read, especially ones that introduce mathmatics of a particular theory. I can handle (some) hard math, as long as the author shows how the equations are derived from something I'm familiar with. If you can think of anything else (not just BH theory), or come across anything, just let me know. Thanks!