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Does Hawking deserve a Nobel prize for his singularity theorem? 
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#37
Jan2410, 05:38 PM

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#38
Jan2410, 06:27 PM

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#39
Jan2410, 09:09 PM

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Let's assume one of your infalling coordinate systems and that the Earth is falling into a massive object. The massive object will not form an event horizon. Where are the applicable coordinate systems where we can say "lookie here. This is a picture of an accreation disk of a black hole." I believe I've answered your questions. Will you answer mine? 


#40
Jan2410, 10:28 PM

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If so, someone could make the same sort of argument about the Rindler horizon, since after all, an accelerating observer who remains outside the horizon (like one of the ones at fixed coordinate position in Rindler coordinates) will never see anything cross it, the only way to see light from an event on the Rindler horizon is to cross the horizon yourself (which should not be too surprising, since from the perspective of an inertial frame the 'Rindler horizon' is just one edge of a future light cone). Note that the relationship between Rindler coordinates (where the Rindler horizon is at fixed coordinate position and it takes an infinite coordinate time to reach it) and inertial coordinates (where the horizon is moving outward at the speed of light and can be crossed in finite time) is very closely analogous to the relationship between Schwarzschild coordinates and KruskalSzekeres coordinates (where the event horizon expands outward at the speed of light). So if some accelerating observer who remained forever outside the Rindler horizon seriously argued that worldlines simply "end" before reaching the proper time T where they are supposed to cross it, what would your response be? I don't see how your position is any less implausible. A: Too vague. Depends if you are talking about coordinate time in some system, or proper time of some clock...and of course it also depends on physical specifics like the mass of the black hole, the point of the collapse you want to start counting down from, etc. Q: How long does it take for its mass to increase? A: You mean, when a new object falls in? I don't think there's any welldefined way to measure the "mass" of an extended object in a coordinateindependent way, so this would presumably depend on your choice of coordinate system too, and how you define "mass" (see this page on the difficulty in defining 'energy' in GR in a nonlocal sense, since mass and energy are equivalent the problems should be the same) Q: What is the age of the universe? A: Again depends on what coordinate system/clock you use, but the most common definition uses a coordinate system whose definition of simultaneity is such that the universe's density is about the same everywhere at a give coordinate time (the average rest frame of the cosmic microwave background radiation), and whose time coordinate matches up with the proper time of a clock that remains at rest in this system. In this case the universe's age since the Big Bang is estimated at 13.7 billion years. Q: What is the theoretical justification for claiming accreation disks, jets, and other evidence of black holes are not also evidence of precollapsed dense masses? A: Because as long as you accept GR, and you accept the principle of "geodesic completeness" which says geodesics shouldn't just "stop" at some finite proper time when it's possible to extend the spacetime manifold in a way that allows them to continue and which respects the Einstein Field Equations everywhere, then for a sufficiently massive object collapsed below a certain radius, it can be proved that an event horizon must form and that whatever's inside cannot be a stable dense mass but will collapse into a singularity (that's what the singularity theorems mentioned at the start of the thread are all about). 


#41
Jan2410, 11:17 PM

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Without jumping through the horizon, the closest I've seen is to try to verify that the metric is the Kerr metric close to the event horizon "Gravitational waves would probe nonlinear gravity and could reveal small corrections, such as extra longrange fields that arise in unified theories, deviations of the metric around massive black holes from the Kerr solution ..." http://arxiv.org/abs/0903.0100 


#42
Jan2510, 04:56 AM

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AB 


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#44
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#46
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#47
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