# Tagged Questions

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### Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...
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### Can a value of “length, in meters” be attributed to a pair of ends which are rigid (but not at rest) to each other? [duplicate]

The definition of the SI base unit "metre" [1] doesn't seem to rule out explicitly that a certain value of "length, in meters" could be attributed to a pair of ends which are rigid to each other, but ...
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### If two ends were a certain “length” apart were they therefore at rest (or at least rigid) to each other? [closed]

Considering the definition of the SI unit of "length" [1] and [2 (" method a.")] I'm missing any requirements about the two "ends" of the required "path travelled by light" being "at rest to each ...
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### Can we derive the relation between proper time and the spacetime interval?

In GR, it's usually taken for granted - or as a definition - that the time measured by an observer's clock is related to the geometry in a very simple way, $d\tau^2 = |ds^2|$. This is easy enough to ...
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### How to express “curvature scalars” in terms of "discrete curvature values $\kappa_n$?

We know from MTW [1] and Synge [2] how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
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### Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
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### What is a geometrical object?

From the Wikipedia link for Geometry: Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
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### Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
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### Limit on velocity in Minkowski Spacetime geometry

Let A be a rocket moving with velocity v. Then the slope of its worldline in a spacetime diagram is given by c/v. Since it is a slope, c/v = tan(theta) for some theta > 45 and theta < 90. Does ...