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Try ezz integral
The line element
ds² = −c² dt² + (dx − vₛ f(rₛ) dt)² + dy² + dz²

carries a bubble of ordinary Minkowski spacetime at any chosen speed vₛ.

The regulating function f(rₛ) equals one throughout a sphere of radius R centered on the ship and falls smoothly to zero across a thin wall. Occupants therefore remain at rest with respect to the interior geometry.

The geometry itself contracts ahead of the bubble and expands behind it, so the whole region can outrun light as seen from far away.

Miguel Alcubierre wrote the metric in 1994. Special relativity is left intact because the motion never occurs locally.
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Try Adv 2016 limits Q. Expecting different approaches ✌️
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Ezz ✌️
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F=ma ☮️.pdf
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F=ma by Ishaan🗿 X Reimannix ☮️
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Based on JEE Advanced 2016 PYQ
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Comprehensive career roadmap.pdf
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