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DAirey
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I have a surface defined by the quadratic relation:$$0=\phi^2t^4-x^2-y^2-z^2$$Where ##\phi## is a constant with units of ##km## ##s^{-2}##, ##t## is units of ##s## (time) and x, y and z are units of ##km## (space). The surface looks like this:
Since the formula depends on the absolute value of ##t##, is it possible to create a metric to describe this surface? If so, what would the metric be (it seems to me that the metric would have to be a function of time such that ##ds^2(t)=<some expression>##).
Since the formula depends on the absolute value of ##t##, is it possible to create a metric to describe this surface? If so, what would the metric be (it seems to me that the metric would have to be a function of time such that ##ds^2(t)=<some expression>##).
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