Main Question or Discussion Point
Hi, the trace of the extrinsic tensor K(Myu,Nu) in Alcubierre metric, relative to the foliation normal vector is non zero on the front x=rs+R and rear x=rs-R "walls". This is the normal volume component Tr =k(1,1)+k(2,2)+k(3,3) and should affect the Ricci tensor in Lorentzian/Minkowsky 4D. How do we know that the Weyl tensor is also zero out of the walls ? In order for the middle of the bubble to experience 0 g, all elements of the Riemann tensor have to be zero, is that correct ? In other words, does gravity vanish out of the walls or only Ricci tensor vanishes our of the walls ? If it is only the Ricci tensor then gravity is not close to zero at x=rs as claimed.