
#37
Sep1811, 05:10 PM

P: 42





#38
Sep1811, 08:16 PM

Physics
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PF Gold
P: 5,505

First, we're not necessarily talking about a runaway collapse, just that when the body reaches a new static equilibrium after some energy has been added from an external source, the body's radius, if its mass is high enough (ten to a hundred times the mass of Jupiter, or more), will be smaller, not larger. So we're comparing static equilibrium configurations with slightly different total energy. Second, to know whether a given configuration is in static equilibrium, we need the equation of state of the matter in the body. My point was that the equation of state is different for degeneracy pressure than for normal kinetic pressure; the dependence of pressure on temperature is much weaker if the pressure is degeneracy pressure than if it is kinetic pressure. That means that raising the temperature doesn't increase the pressure much, if at all, when the pressure is degeneracy pressure; but it also means that degeneracy pressure can increase a lot without increasing the temperature much, if at all. Third, I'm not sure what you mean by "storing energy in pressure". Pressure has the units of energy density, but that doesn't mean it *is* energy density. Pressure happens to be proportional to energy density in an ideal gas, as we saw earlier, but that doesn't mean it "counts" as energy density. In terms of the stressenergy tensor, pressure is the diagonal spacespace component, while energy density is the timetime component; they are physically distinct. And of course, the ideal gas equation of state is a very special case; for other equations of state, pressure may not even be proportional to energy density. If the pressure is degeneracy pressure, as I said above, the pressure will be only weakly, if at all, dependent on the temperature (hence energy density). 



#39
Sep1911, 05:36 PM

P: 42

We are all familiar with the experiments that verify that time slows down. But the logical extreme of that is "time stops". If there is a region of space where time stops, what is the implication of that? And what does it mean if more mass packs on top of mass where time has stopped? If time has stopped on one particular chunk of mass, how can other mass pack on top of it? Packing means that time is moving, not stopped. A philosophical conundrum, yes? Of course, I could be wrong. Is this what you are trying to get at? 



#40
Sep1911, 09:58 PM

Physics
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PF Gold
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#41
Sep2011, 05:50 AM

PF Gold
P: 1,376

But argument about reduction in radius was different. It was about change in mass of object not about change in total energy of system. As I understand that argument it assumes that system is at 0 temperature and there is only degeneracy pressure present and no kinetic pressure. So there is certain level of total energy when equilibrium is reached (all extra energy is radiated away) and consequently certain radius for that state. Degeneracy pressure does not depend from temperature at all. If you increase temperature of degenerate matter there appears nonzero kinetic pressure but it's contribution to summary pressure is rather small. That's the reason why pressure of degenerate matter depends very little from temperature (not because degeneracy pressure depends weakly from temperature). My formulation probably was not very clear. Maybe "storing energy in compression" is more correct. 



#42
Sep2011, 07:01 AM

P: 42





#43
Sep2011, 01:31 PM

Physics
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PF Gold
P: 5,505

For example, consider an "average" particle in the Earth's atmosphere, compared with a small test object in a freefall orbit about the Earth at the same altitude. (We'll ignore the fact that an object in orbit inside the atmosphere would experience drag and would not stay in orbit; if you like, we can consider the second particle to be in orbit about a "twin Earth" that has no atmosphere but is otherwise identical to Earth.) The object in the freefall orbit obeys the virial theorem in the simple form you stated it: its kinetic energy is minus onehalf its potential energy. But the particle in the atmosphere does not; its kinetic energy is much *less* than minus onehalf its potential energy, because its potential energy is the same (the altitude is the same), but its kinetic energy is just the temperature of the atmosphere in energy units, which is much smaller than the equivalent "temperature" of a particle in orbit. Put another way, the average velocity of a particle in the atmosphere is much *less* than the orbital velocity at the same altitude. So the virial theorem in the simple form you gave does not apply to a fluid with nonzero pressure. 



#44
Sep2011, 01:32 PM

Physics
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#45
Sep2011, 01:42 PM

P: 1,555





#46
Sep2011, 02:22 PM

Physics
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#47
Sep2011, 03:48 PM

P: 1,555





#48
Sep2011, 05:01 PM

P: 42

I'm starting to feel like I may be hijacking this thread. In any case, keepit seems to have lost interest. 



#49
Sep3011, 07:33 AM

P: 186





#50
Sep3011, 08:04 AM

C. Spirit
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[/tex] which is clearly finite. You can also verify this for observers who don't start from infinity and still find that it takes finite proper time to cross the event horizon. 



#51
Sep3011, 10:48 AM

P: 1,555





#52
Sep3011, 10:57 AM

C. Spirit
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#53
Sep3011, 11:09 AM

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PF Gold
P: 4,860

1) A distant observer never sees (gets any indication from light or any source) anything pass the event horizon. They also see time freeze for matter approaching the event horizon. 2) A free falling body will cross the event horizon in finite proper time, reaching the singularity in finite proper time. 


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