TA30

==Chapter 30 - The Armada==
LCS verwirrter Fragesander
Beagle Class Exploration Cruiser
Deep Periphery
3169 CE
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["...supernova events will give us something nobody's had."]
Rear Admiral Clarissa Ngo waited for the scientific team to catch up.  "What?"
"Tons of exotic matter boys and girls." she said.  "In the twenty-first century, there was an historical competitor to Kearney and Fuchida, but they couldn't find, beg, borrow, steal or wish into existence tons of the right kind of high-energy exotic matter."
She made a gesture, and the flat renders and holo displays in the Lab module lit up.
Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time t, with the metric taking the following general form:
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{\displaystyle ds^{2}=-\left(\alpha ^{2}-\beta _{i}\beta ^{i}\right)\,dt^{2}+2\beta _{i}\,dx^{i}\,dt+\gamma _{ij}\,dx^{i}\,dx^{j},}{\displaystyle ds^{2}=-\left(\alpha ^{2}-\beta _{i}\beta ^{i}\right)\,dt^{2}+2\beta _{i}\,dx^{i}\,dt+\gamma _{ij}\,dx^{i}\,dx^{j},}
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,
γij is a positive-definite metric on each of the hypersurfaces.
The particular form that Alcubierre studied[4] is defined by:
{\displaystyle {\begin{aligned}\alpha &=1,\\\beta ^{x}&=-v_{s}(t)f{\big (}r_{s}(t){\big )},\\\beta ^{y}&=\beta ^{z}=0,\\\gamma _{ij}&=\delta _{ij},\end{aligned}}}{\displaystyle {\begin{aligned}\alpha &=1,\\\beta ^{x}&=-v_{s}(t)f{\big (}r_{s}(t){\big )},\\\beta ^{y}&=\beta ^{z}=0,\\\gamma _{ij}&=\delta _{ij},\end{aligned}}}
where
{\displaystyle {\begin{aligned}v_{s}(t)&={\frac {dx_{s}(t)}{dt}},\\r_{s}(t)&={\sqrt {{\big (}x-x_{s}(t){\big )}^{2}+y^{2}+z^{2}}},\\f(r_{s})&={\frac {\tanh {\big (}\sigma (r_{s}+R){\big )}-\tanh {\big (}\sigma (r_{s}-R){\big )}}{2\tanh(\sigma R)}},\end{aligned}}}{\displaystyle {\begin{aligned}v_{s}(t)&={\frac {dx_{s}(t)}{dt}},\\r_{s}(t)&={\sqrt {{\big (}x-x_{s}(t){\big )}^{2}+y^{2}+z^{2}}},\\f(r_{s})&={\frac {\tanh {\big (}\sigma (r_{s}+R){\big )}-\tanh {\big (}\sigma (r_{s}-R){\big )}}{2\tanh(\sigma R)}},\end{aligned}}}
with arbitrary parameters R > 0 and σ > 0. Alcubierre's specific form of the metric can thus be written
{\displaystyle ds^{2}=\left(v_{s}(t)^{2}f{\big (}r_{s}(t){\big )}^{2}-1\right)\,dt^{2}-2v_{s}(t)f{\big (}r_{s}(t){\big )}\,dx\,dt+dx^{2}+dy^{2}+dz^{2}.}{\displaystyle ds^{2}=\left(v_{s}(t)^{2}f{\big (}r_{s}(t){\big )}^{2}-1\right)\,dt^{2}-2v_{s}(t)f{\big (}r_{s}(t){\big )}\,dx\,dt+dx^{2}+dy^{2}+dz^{2}.}
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
{\displaystyle -{\frac {c^{4}}{8\pi G}}{\frac {v_{s}^{2}\left(y^{2}+z^{2}\right)}{4g^{2}r_{s}^{2}}}\left({\frac {df}{dr_{s}}}\right)^{2},}{\displaystyle -{\frac {c^{4}}{8\pi G}}{\frac {v_{s}^{2}\left(y^{2}+z^{2}\right)}{4g^{2}r_{s}^{2}}}\left({\frac {df}{dr_{s}}}\right)^{2},}
where g is the determinant of the metric tensor.
Thus, because the energy density is negative, one needs exotic matter to travel faster than the speed of light.[4] The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and also to keep open the "throat" of a wormhole) is thought to be impractical.[citation needed] According to writer Robert Low, within the context of general relativity it is impossible to construct a warp drive in the absence of exotic matter.[10]
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"This." Clarissa said.  "There are remnant manufacturing facilities in the system the Tranh Truk Ngo is trapped in, hyperspace is all kinds of ****** up, and their KF drive is toast...but the theorems were never tested.  The closest anyone got to it, is the working theory behind black-boxes, and that's only a tangent off the original equations. Alcubierre's work wound up one of those dusty boxes in the Special Operations office, because it's something we never got to test, but if it works, could be revolutionary."
"Oh god, and you think we'll be able to test it now?" Doctor Cummings asked
"I think Mike Nguyen might be able to-assuming his team, ship, and the refugees he's picked up survived.  I know we put a full maintenance shop on that particular destroyer as part of her refit for long-range work.  They also have a few Ionized particle shield gennies and a few of our other tricks...and we're not going to be losing anything if I ask him to try to engineer it and capture some exotic matter for us."
"That...is completely insane, Admiral." said Doctor Cummings
"Yeah, it is.  Sometimes science isn't asking 'why', it's asking 'why not?', you dig, Doctor Cummings? We have for right now a communications link to a ship we can't rescue. Who can't escape and is facing in the next three weeks a violent and destructive cosmic event from which they won't be able to escape anyway.  So...why not?  There are only upsides to this. Guys-we either sit and listen to a good man and great people die slowly or we give them a chance to save themselves while making the history books ten times over."
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