> Special Relativity can be summed up in the sentence: “We live in a spacetime which is an M4 manifold with a hyperbolic Lorentz metric of signature (+−−−)”. General Relativity can be stated accordingly: “The Universe is an M4 manifold with a Riemannian metric of signature (+−−−)” which is a solution of the Einstein equation:Rμν−12Rgμν+Λgμν=χTμν.

It sounds like you get anti-gravity for free along the way to getting superluminal travel.