Alcubierre metric and General Relativity

[Orion1]

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?
[/Color]
Reference:
Alcubierre metric - Wikipedia

 

[haushofer]

Plug your ansatz in Mathematica and see what the constraints on your parameters are.