Heading One

Heading Two, Italic

Heading Three

Heading Four

Heading Five

Heading Six

Font family $sans-serif => { nimbus-sans-condensed, "Helvetica Neue LT Std", "Helvetica Neue", Helvetica, "Neue Haas", Arial, sans-serif; } — Nimbus Sans provisioned by Typekit (loading 400 and 700, italic forced)

Font family $serif => { Spectral, Garamond, Georgia, "Times New Roman", serif; } — Spectral provisioned by Google Fonts (loading 400, 400i, 500, and 600)

Introductory paragraph style, it is now clear that T can be made as small as we want by increasing the value of a. Since a round trip will only take twice as long, we find that we can be back in star A after an arbitrarily small proper time, both from the point of view of the spaceship and from the point of view of the star.

Default paragraph style, the spaceship will then be able to travel much faster than the speed of light. However, as we have seen, it will always remain on a timelike trajectory, that is, inside its local light-cone: light itself is also being pushed by the distortion of spacetime. A propulsion mechanism based on such a local distortion of spacetime just begs to be given the familiar name of the “warp drive” of science fiction.

Small paragraphy style, the metric I have just described has one important drawback, however: it violates all three energy conditions (weak, dominant and strong [3]). Both the weak and the dominant energy conditions require the energy density to be positive for all observers. If one calculates the Einstein tensor from the metric (8), and uses the fact that the four-velocity of the Eulerian observers is given by:

• It is easy to understand the geometry of our spacetime from the previous expressions. First, from equation (5) we see that the 3-geometry of the hypersurfaces is always flat. Moreover, the fact that the lapse is given by α = 1 implies that the timelike curves normal to these hypersurfaces are geodesics
• Id est, the Eulerian observers are in free fall. Spacetime, however, is not flat due to the presence of a non-uniform shift.
• Nevertheless, since the shift vector vanishes for rs ≫ R , we see that at any time t spacetime will be essentially flat everywhere except within a region with a radius of order R, centered at the point (xs(t), 0, 0) .

Block Quote: A propulsion mechanism based on such a local distortion of spacetime just begs to be given the familiar name of the “warp drive” of science fiction.