§lîñk€¥™ Posted January 22, 2003 Posted January 22, 2003 Black holes (BH from hereon) are curious objects. The curious thing about them is that if you could watch something falling towards a BH you would never see it cross the event horizon (EH from hereon). For example, if I was watching a clock fall toward a BH, I would notice that it slows down more and more as it gets closer to the EH (it also would get dimmer and dimmer). This will always be the case from any view outside the EH no matter how long you wait. The clock will never be seen to cross the EH. It will slow down and then appear to be frozen (it won't be frozen but will be moving imperceptably). So does the clock ever actually cross the EH of a BH? I say it doesn't. My reasoning for my conclusion: Reason #1: Imagine you are freely falling feet first towards a BH (we'll ignore the "spaghettifying" effects of the increasingly extreme gravity it's just the persepective that I want to deal with). Just below your feet (and closer to the BH than yourself) is a clock also in free fall. ie. as you fall the clock will always be below you and falling at a slightly faster rate because it is experiencing a greater acceleration due to the higher gravity it is experiencing than yourself. As you get closer and closer to the EH you watch the clock. It starts to slow down. This is because as you get closer to the EH the gravity gradient increases. However, you will never see that clock cross the EH as described above. But dig this, not only that, but you are still above the clock. You are still farther away from the EH than the clock. So if you never see the clock cross the EH and you are always farther from the EH than the clock, then you never cross the EH. Reason #2: According to Stephen Hawking a BH isn't entirely black. Due to Heisenberg Uncertainty it is able to lose mass. They "evaporate", and have a temperature which is inversely proportional to their mass. ie. the more massive they are, the less they radiate and the colder they are, and vice versa. Rough figures indicate (1) that for a BH with a mass of 3 to 4 solar masses will take something in the region of 10^60 years to completely evaporate. This is an extraordinarily long time (we don't even know for sure if the Universe will live that long but for my purposes here we'll assume that it will). That 10^60 years calculation is made from the perspective of an outside observer, however, remember when we watch the clock fall towards a black hole we will never see it cross the EH. In effect, we could watch the black hole for 10^60 years and we will never see the clock cross the EH whether we are in stationary orbit above the BH or are falling behind the clock towards the BH. According to GR there is a point above the EH of a BH where the dilation is not only equal to the lifespan of the BH, but greater than the lifespan of the BH. In fact, GR says that there will be a dilation above the EH that is equal to the entire lifespan of the Universe! ie. there is always a point above the EH that would make the black hole evaporate before you get to it's EH. My Conclusion: Black holes cannot eat anything. In fact, I'm going to stick my neck out (and hope I don't lose my head!) and say that the current picture of black holes is wrong, and if they do exist, then they cannot "eat" and "starve to death". If you can find some holes in my reasoning then please point them out to me. (1) - 3-4 solar masses takes 1060 years to evaporate figures from Stephen Hawking's book "A Brief History of Time". kind regards
fafalone Posted January 22, 2003 Posted January 22, 2003 Once a black hole forms it has an event, but when objects "fall in", the black hole expands; but how is this possible if time stops and the object that fell in never passes it?
Radical Edward Posted January 22, 2003 Posted January 22, 2003 this seems somewhat inconsistent with calculated results. It#'s an interesting sounding paradox (if indeed it is one) I suggest you chug through the maths before really thinking you're right.
Radical Edward Posted January 22, 2003 Posted January 22, 2003 incidentally slinkey... London , Student.... you don't go to Imperial College do you?
liljohnak Posted January 23, 2003 Posted January 23, 2003 take this for an idea (idea that i havnt chuged the numbers on but an idea that i thought id share) ok say that you were inside an EH would you even know it? I think not because how much faster can you travel than light speed. so everything will be on a singular clock time. but the only thing is is that you would be stuck inside a glass ball that you can see and know what is happening around you outside but you cant get passed it. I got a ? where could i go to c the numbers they crunched to in theory prove the exsistance of a BH.
Radical Edward Posted January 23, 2003 Posted January 23, 2003 get an elementary book on GR and you can demonstrate the existance of a black hole. and yes yo uwould know about it.... since you couldn't look downwards and seea anything. actually I have a thought that life couldn't actually exist inside a black hole, but then I don't know much bout GR ,and I'm not going for idle conjecture.
Giles Posted January 23, 2003 Posted January 23, 2003 Um, I could be very badly wrong, but i think the fact that time slows down for the particle as it drops towards the event horizon doesn't actually make a difference to its speed of motion as observed by someone else.
JaKiri Posted January 23, 2003 Posted January 23, 2003 Originally posted by Giles Um, I could be very badly wrong, but i think the fact that time slows down for the particle as it drops towards the event horizon doesn't actually make a difference to its speed of motion as observed by someone else. Relative to your defined rest frame, you're always going at the speed you think you're going, as the Lorenz transforms for time and length cancel. As for stationary observers, you need to use this forumula: combined recession speed = (a + b) / (1 + ab/c^2) Where the velocities of the objects are a and b. All this translates to 'No, your supposition is incorrect' (at the original post, not Giles's). Also: iirc, physical laws are invarient under acceleration/gravitational fields.
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Wow, didn't expect such a lot of replies so quickly. Thanks for taking the time to read my ideas. I just want to add some comments that may serve to make people think again on some of their replies. A black hole (BH) is charactersed by it having an event horizon. The event horizon (EH) "marks the spot" where the gravity becomes so extreme that not even light can escape from beyond it. The important thing to remember is that General Relativity (GR) is a classical theory. ie. there is a continual "spectrum" that leads from flat space to the event horizon. This means that any and every point between flat space and the event horizon has an associated gravity and time dilation. At the event horizon time is dilated infinitely. However, classical GR demands that to reach that point of infinite dilation one must cover every point that leads to it (no, I'm not resurrecting Zeno ). You could get to a point just outside the EH that equates to a time dilation of 1sec taking 10^1,000,000 seconds for an observer in flat space. But don't forget, GR demands that I must take every step on the road to infinity. This means that as I move infinitesimally closer to the EH I enter a higher time dilation. The next moment the dilation would be even worse and might calculate to 1 sec taking 10^1,000,000,000 seconds. And again. The next moment the dilation might be 10^1,000,000,000,000. And so on all the way to infinity. One thing that is clear is that the closer you get the the EH the steeper this dilation gradient is. ie. moving 1mm towards the BH when you are far from it doesn't make for much of a change of time dilation. But if you are 1mm above the EH a movement of 1mm would make for a massive change in dilation. In fact, that last 1mm would involve an infinite change in dilation. An infinite amount of time is plenty for a black hole of any size to have evaporated by Hawking Radiation. Anyways, just some more thoughts to ponder. kind regards
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by Radical Edward this seems somewhat inconsistent with calculated results. It#'s an interesting sounding paradox (if indeed it is one) I suggest you chug through the maths before really thinking you're right. I wish I was educated enough to be able to do that. Maybe in 5 years of so. kind regards
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by Radical Edward incidentally slinkey... London , Student.... you don't go to Imperial College do you? No. I wish I could afford to goto any University right now. But I digress... Student on my profile is kind of tongue in cheek in that I study physics (and now math) in my spare time. I use it to indicate that I don't know everything but I am capable of learning. kind regards
JaKiri Posted January 23, 2003 Posted January 23, 2003 Originally posted by §lîñk€¥™ See my first point. PS: If this is from reading Hawking, forget everything and read The Elegant Universe, or preferrably The Feynman Lectures on Physics. SH gets quite a few things wrong.
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by liljohnak take this for an idea (idea that i havnt chuged the numbers on but an idea that i thought id share) ok say that you were inside an EH would you even know it? I think not because how much faster can you travel than light speed. so everything will be on a singular clock time. but the only thing is is that you would be stuck inside a glass ball that you can see and know what is happening around you outside but you cant get passed it. I got a ? where could i go to c the numbers they crunched to in theory prove the exsistance of a BH. This is a little programmable applet that show you what the universe would look from various points above, at, or below the EH of a BH. Click here for some fun physics kind regards
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by MrL_JaKiri As for stationary observers, you need to use this forumula: combined recession speed = (a + b) / (1 + ab/c^2) I could be wrong but I think that only applies in Special Relativity when adding uniform velocities. GR is accelerations and non-uniform velocities. kind regards
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by MrL_JaKiri See my first point. PS: If this is from reading Hawking, forget everything and read The Elegant Universe, or preferrably The Feynman Lectures on Physics. SH gets quite a few things wrong. Hmm, you didn't quote anything so I'm not entirely sure what you are referring to when you say "see my first point". I can assure you I have read more than 1 book on the subject. I found "Black Holes and Time Warps" not only superior to Hawking but brimming with information. Hey, I just had a thought. I wonder if there are any calculations in the notes at the back that could help solve this problem. I'll get back to you on this with what I turn up. kind regards
JaKiri Posted January 23, 2003 Posted January 23, 2003 Originally posted by §lîñk€¥™ Hmm, you didn't quote anything so I'm not entirely sure what you are referring to when you say "see my first point". I can assure you I have read more than 1 book on the subject. I found "Black Holes and Time Warps" not only superior to Hawking but brimming with information. Hey, I just had a thought. I wonder if there are any calculations in the notes at the back that could help solve this problem. I'll get back to you on this with what I turn up. kind regards About the invariance of measured speed.
Giles Posted January 23, 2003 Posted January 23, 2003 Why would time be dilated infinitely at an event horizon? The point of the horizon is defined by the escape velocity exceeding light speed (or the schwarzchild radius iirc). It's not like you're experiencing infinite acceleration/force.
JaKiri Posted January 23, 2003 Posted January 23, 2003 Originally posted by Giles Why would time be dilated infinitely at an event horizon? The point of the horizon is defined by the escape velocity exceeding light speed (or the schwarzchild radius iirc). It's not like you're experiencing infinite acceleration/force. Schwarzchild-agogo
§lîñk€¥™ Posted January 23, 2003 Author Posted January 23, 2003 Originally posted by Giles Um, I could be very badly wrong, but i think the fact that time slows down for the particle as it drops towards the event horizon doesn't actually make a difference to its speed of motion as observed by someone else. I think you are correct. However, it's speed of motion isn't the critical factor. The critical factor is that it has to take every step on the road to infinite time dilation. No matter how far away from the BH you are, you still have to cover every step on that road to infinity. The important thing to remember is that the lifespan of the BH (I used the 10^60 years figure in my example) is as measured from flat space at infinity above the EH. As you move towards the BH you would have to revise this calculation. You are in a different frame of reference to the BH. As you move closer to the BH your calculation for the lifespan of the BH would be revised down (this is an assumption on my part and one of the things that I would like someone better in the know than myself to verify or correct me on). As you get closer and closer to the BH your revision would make the BH's lifespan shorter and shorter. My reasoning follows: I am in flat space at infinity above the BH. You are in your spaceship between me and the BH. I am looking at the clock on your spacehip (we'll ignore the mechanism for this and the ensuing time delays/shifting of frequency of the signals reaching me/climbing out of a gravity well, it's just time I want to discuss here). Your clock is ticking half as fast a mine. You look back at me at my clock. My clock is ticking twice as fact as yours. (NB. In GR we don't get the same symmetry as SR because GR is accelerated reference frames and these break the symmetry). From my perspective I calculate the BH will exist for 10^60 years. How long do you calculate it will exist, bearing in mind that my calculation was done from a frame of reference that is moving (temporally) twice as fast relative to you? kind regards
JaKiri Posted January 23, 2003 Posted January 23, 2003 Originally posted by §lîñk€¥™ I'm going to come back to this topic after I've done some research; I haven't the experience with General that I have with Special.
liljohnak Posted January 24, 2003 Posted January 24, 2003 why arent we allowed to move at light speed? we can get very close but never get there. why cant we reach absolute 0? why cant we reach the event horizon? are these somehow related why we cant reach these extremes?
JaKiri Posted January 24, 2003 Posted January 24, 2003 Originally posted by liljohnak why arent we allowed to move at light speed? we can get very close but never get there. why cant we reach absolute 0? why cant we reach the event horizon? are these somehow related why we cant reach these extremes? Not really; we can't reach light speed because it would require infinite energy (the mass of something with a non-zero rest mass will increase to infinity at light speed) and we can't reach absolute zero because it would require an infinite number of finite steps.
§lîñk€¥™ Posted January 24, 2003 Author Posted January 24, 2003 Originally posted by MrL_JaKiri I'm going to come back to this topic after I've done some research; I haven't the experience with General that I have with Special. I'm the same. I know SR pretty well but GR is a little vague to me. I too will be researching this and will let you know if I turn up anything that confirms or refutes my suggestions. kind regards
§lîñk€¥™ Posted January 24, 2003 Author Posted January 24, 2003 Originally posted by liljohnak why cant we reach absolute 0? I read an article sometime back, I think in New Scientist (or maybe Scientific American) that, simply put, said the reason we cannot reach absolute zero is because in trying to remove the last quanta of energy we have to introduce energy into the system which, of course, then replaces the energy we are trying to remove. I'll try and find this article if anyone is that interested (but only if someone specifically request it). kind regards
fafalone Posted January 24, 2003 Posted January 24, 2003 Well if you take the gas laws approach you see that on the graph of temperature and volume, absolute zero would require a volume of zero; and since m = vd, the atoms would also be required to have zero mass.
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