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Proper spacelike distance in Alcubierre manifold

How do I find the proper spacelike $x$-coordinate on a constant $t$ hypersurface in the two dimensional Alcubierre manifold? The metric is given by $$\mathrm{d}s^2=(v^2f^2-1)\mathrm{d}t^2-2vf\mathrm{d}...
user345249's user avatar
2 votes
2 answers
183 views

Calculating proper volume in the Alcubierre spacetime

I'm trying to calculate the proper volume of a portion of the alcubierre spacetime to see how it compares to the euclidean volume element. As I understand it, the proper volume element in cartesian ...
user345249's user avatar
0 votes
1 answer
229 views

Computing Riemann tensor components for Alcubierre metric

I am currently trying to compute the Riemann tensor components for the Alcubierre metric, and already, on the computation of the first component, I'm running into some issues. The trouble component in ...
Carmenifold's user avatar
8 votes
3 answers
2k views

Why Can We Observe Space Curvature / Warping At All?

I don't understand why we are able to see and measure curvature / warping of space at all. Space as I understand it determines distances between objects, so if space were "compressed" or warped, ...
Arc's user avatar
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