cianfa72's latest activity
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cianfa72 reacted to Paul Colby's post in the thread Graduate Gravitational wave propagation in GR - follow up with
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At this point I find it instructive to consider some numbers. A round trip time for light in a 4km long interferometer is, $$... -
cianfa72 replied to the thread Graduate Topological constrains for the solutions of EFE.Ok, so in the case of SC spacetime geometry, does exist a maximal analytic extension that can be obtained starting from the SC chart and...
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cianfa72 replied to the thread Graduate Gravitational wave propagation in GR - follow up.ok yes. Yes. Just to be clear: the metric isn't stationary (in the spacetime region where the GW passes). The proper length of each arm...
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cianfa72 replied to the thread Graduate Topological constrains for the solutions of EFE.Ah ok. So for example it is part of Schwarzschild chart's specification that it covers the open region of spacetime outside the horizon...
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cianfa72 replied to the thread Graduate Topological constrains for the solutions of EFE.I mean....if I give you an expression for the metric tensor field in some chart and nothing else, you can't say in which region of...
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cianfa72 replied to the thread Graduate Gravitational wave propagation in GR - follow up.Ok, this because for a worldline at rest in TT gauge coordinates, i.e. ##(t, x_0, y_0,z_0)##, the geodesic equation becomes: $$ \frac...
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cianfa72 replied to the thread Graduate Topological constrains for the solutions of EFE.Another point related to this. The Lie commutator of any pair of coordinate vector fields (say X,Y,Z,T) vanishes hence the frame field...
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cianfa72 reacted to Paul Colby's post in the thread Graduate Gravitational wave propagation in GR - follow up with Like.
In the TT gauge (coordinates), the metric stain, ##h_{ab}##, only has spatial components, ##h_{xx}, h_{xy},\cdots##, are non-zero and...
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cianfa72 reacted to pervect's post in the thread Graduate Gravitational wave propagation in GR - follow up with Like.
My understanding is that the test masses in Ligo essentially follow space-time geodesics (aka are in free fall), ignoring some of the...
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cianfa72 replied to the thread Graduate Gravitational wave propagation in GR - follow up.Ok, so the timelike congruence "at rest" in TT gauge coordinates (i.e. the congruence described by timelike worldlines with fixed...
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cianfa72 posted the thread Graduate Gravitational wave propagation in GR - follow up in Special and General Relativity.I'd like to consider again what discussed in this Gravitational wave propagation in GR. The analysis of GWs' LIGO measurements is...
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cianfa72 reacted to PeterDonis's post in the thread Graduate Topological constrains for the solutions of EFE with Like.
Yes, I've already agreed with that; the only possible topologies are ##S^3## and ##R^3##. The cylinder you describe would be ##S^2...
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cianfa72 reacted to jbergman's post in the thread Graduate Equivalent definitions of tensor field with Like.
Yes. In Lee's book, he defines a smooth functor with which you can lift constructions on vector spaces to vector bundles...
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cianfa72 replied to the thread Graduate Equivalent definitions of tensor field.Oops yes, a twice covariant tensor field eats two vector fields :-) Yes, definitely. Look now at the writing ##T^*M \otimes T^*M##...
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cianfa72 reacted to jbergman's post in the thread Graduate Equivalent definitions of tensor field with Like.
The second doesn't look correct. It should be a multilinear function of sections of the tangent space, not the cotangent space. It's...