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comment Interpreting $Q_i=\partial_{\nu}T^{i \nu}$ from dust
I'd suggest first looking at what $Q^{\mu}U_{\mu}$ is, and then interpret what's left over.
Apr
27
comment Gross “temperature” of a globular cluster
@CuriousOne: sure, but it doesn't matter if there can't be a heat exchange.
Apr
27
comment Gross “temperature” of a globular cluster
@CuriousOne: the only way that it would be useful to compare them is to see clusters collide and have some sort of energy you could get out... Which, come to think of it, might actually be physically relevant.
Apr
27
comment Gross “temperature” of a globular cluster
The second point is true of the Earth's atmosphere, though, and one would surely say that it's ridiculous to say that the atmosphere doesn't have a temperature.
Apr
27
comment Equivalence of definitions of ADM Mass
@alphanzo: I know for a fact that it is unrelated to anything asymptotic. The formula is true for finite-area surfaces.
Apr
27
comment Equivalence of definitions of ADM Mass
@alphanzo: You're right, and looking at it, I'm almost certain the missing term has to do with the difference between the three-metric and the four-metric. The christoffel symbols should be expended as $g_{ab}$ terms, not $\gamma_{ab}$ terms, but I dont' have th etime to fix it righ tnow.
Apr
22
comment Tension and friction. Cool question
The rope is attached to $B$. Therefore, there is no force from the rope on $A$. There must be another mistake in your work.
Apr
22
comment If Black Holes Consume Space What Is The Space Traversing?
So it will be hard to give an answer without resorting to being very technical, and once you have done so, the layman's translation of the result will likely be unsatisfying.
Apr
22
comment If Black Holes Consume Space What Is The Space Traversing?
It will be very difficult to come up with a coherent answer to this question, because it presupposes coming up with a concrete definition of what it means for space "to move", and once you operationally do so, the answers will amount to things like "the space gets contracted into the singularity" or "the space moves out to infinity", or "the space gets compressed inside the horizon, but does not go away", that aren't especially informative.
Apr
20
comment The ratio of masses in an elastic collision
The correct ratio is one. Think about what happens when one billiard ball hits another completely head-on without any spin effects.
Apr
20
comment Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?
@ValterMoretti: you improved my answer, irrespectively. :)
Apr
20
comment Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?
But I should have said tha tthe EOM are lorentz covariant, not invariant.
Apr
20
comment Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?
@ValterMoretti: yes, I didn't say the path was the same, just that the value of the action is necessarily the same, so Lorentz transforms map solutions of the EOM to other solutions of the EOM.
Apr
18
comment What Color Are Black Holes Really? (Yes, a serious question)
But a zero degree black hole is either extremal or has infinite mass, so I don't see how it applies to this problem.
Apr
15
comment Inequivalent matter actions with the same stress-energy tensor in general relativity
Also, does the action have to stay Lorentz-invariant? because terms with factors of $\frac{1}{\sqrt{g}}$ will help you out here, but it will make the integrand of S not a volume element.
Apr
15
comment What happened to the black hole firewall theory?
(for completeness, the event horizon is "the boundary of the past of the singularity")
Apr
15
comment What happened to the black hole firewall theory?
Ironically, the apparent horizon is defined in a way that is closer to the popular science notion of what an event horizon is than the event horizion itself -- the apparent horizon is the closed surface from which light marginally cannot escape.
Apr
15
comment What happened to the black hole firewall theory?
There's no dumping the event horizon for the apparent horizon. They are two distinct things that were known about in the '70s. The main problem is that if you are looking at a black hole that completely evaporates, depending on the details of the evaporation you don't even necessarily have an event horizon.
Apr
14
comment Straight lines in general relativity
You have to treat this more abstractly than that. You can't even embed an arbitary 2-dimensional space into three dimensional flat space. See the hyperbolic plane. The reason why intrinsic geometry is so important is because you can't rely on the embedding to reach conclusions.
Apr
8
comment Can a rotating black hole have a donut-shaped event horizon?
No, the answers to these things are all radically different and have nothing to do with each other.