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Suppose a 2-dimensional space is spanned by the coordinates (v, x) and that the line element is...

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Physics

Suppose a 2-dimensional space is spanned by the coordinates (v,x) and that the line
element is defined by:

ds2 = -xdv2 + 2dvdx

i) Assuming that the nature and properties of the spacetime lineelement still hold,
show that a particle in the negative x-axis can never venture intothe positive
x-axis. That is, show that a particle becomes trapped if it travelsinto the
negative x-axis.
ii) Draw a representative light cone that illustrates how aparticle is trapped.

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