Quote:
Originally Posted by OzMan
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oh i get it now you mean....
where α is the lapse function that gives the interval of proper time between nearby hypersurfaces, βi is the shift vector that relates the spatial coordinate systems on different hypersurfaces and γij is a positive definite metric on each of the hypersurfaces. The particular form that Alcubierre studied (1994) is defined by:
βy = βz = 0
γij = δij
where
and
with R > 0 and σ > 0 arbitrary parameters. With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by