Alcubierre metric and General Relativity

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Alcubierre metric:
ds^2 = \left( v_s(t)^2 f(r_s(t))^2 -1 \right) \; dt^2 - 2v_s(t)f(r_s(t)) \; dx \; dt + dx^2 + dy^2 + dz^2
What formal conditions are required to verify a valid metric solution of the Einstein field equations?

How many possible valid metric solutions are there in General Relativity?
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Reference:
Alcubierre metric - Wikipedia
 
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Plug your ansatz in Mathematica and see what the constraints on your parameters are.
 
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