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The variables used in general relativity to describe the shape of spacetime. If your question is about metric units, use the tag "units", and/or "si-units" if it is about the SI system specifically.

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Since the other answers so far mostly tackle the question of why the hyperbolic rotations do properly represent the Lorentz transformations, I'd like to write a few lines about why they might give a b …
answered Sep 29 '17 by Photon
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Because the mass distribution is spherically symmetric (by assumption, this is what makes the metric Schwarzschild), so the space-time curvature does not depend on the angle, only on the distance from …
answered Feb 14 '17 by Photon
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Your first expression is not well-defined. According to the Einstein summing convention, you sum over double indices, where one index is upper and the other one is lower. Such indices are called silen …
answered Jul 15 '18 by Photon
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You are right, the formula for length contraction is not as simply explained as the analogy in my first answer implied. If you have an extended object, its 4D representation is a strip through space-t …
answered Apr 29 '17 by Photon
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You can use the Tolman metric which is the most general spherically symmetric (but neither homogeneous like FLRW nor static like Schwarzschild) metric. I wrote my Bachelor thesis on a collapsing spher …
answered Jun 9 '17 by Photon
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If you are dealing with spacetime indices (i.e. tensors over the spacetime), then symbols like $\delta^{ab}$ or $\delta_{ab}$ don't make sense. If you lower an index of $\delta^a_b$ you will end up wi …
answered Apr 13 '14 by Photon
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$ds'$ is some function of $ds$ which we want to find: $ds'=ds'(ds)$ We can taylor expand this function: $ds'(ds)=ds'(0)+ads + \mathcal{O}(ds^2)$ for some $a$. Since $ds'$ and $ds$ are both of fir …
answered Jun 7 '17 by Photon
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Let me try an analogy. Back in the early days of America people wanted to measure the exact distance between their flats in New York. As you know, New York has a very regular map, there are streets go …
answered Apr 28 '17 by Photon
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The RW metric describes a space time whose spatial part is expanding, homogeneous and isotropic. Since we think of our universe to be expanding, homogeneous and isotropic, this metric is used in cosmo …
answered Feb 21 '17 by Photon
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One possibility is to substitute the $t_i$ with an imaginary time: $t=i\tilde t$. If you plug this into your interval, it becomes euclidean: $$ds^2=c^2dt^2-dx^2=-c^2d\tilde t^2-dx^2$$ You know that th …
answered May 19 '17 by Photon
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This factor is just the Jacobian determinant which enters an integral if you switch to curvilinear coordinates from Cartesian coordinates which can be defined in a neighbourhood of any point. See also …
answered Apr 14 by Photon