ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j

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$ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Images?q=tbn:ANd9GcSdfhSzzXMymwOgKpeOlGHnfOFSzaySlV8CWx_7wpwWuprmv_CK$

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$ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Images?q=tbn:ANd9GcSv5zmgI_efKgUdR-v_gpz26N4mSIvG2PjkMlGuqTk1wDzVfs4znA$

The Alcubierre metric defines the warp-drive spacetime. It is a Lorentzian manifold, which, if interpreted in the context of general relativity, allows a warp bubble to appear in previously-flat spacetime and move away at effectively-superluminal speed. Inhabitants of the bubble feel no inertial effects. This method of transport does not involve objects in motion at speeds faster than light with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move faster than the ship. As objects within the bubble are not moving (locally) faster than light, the mathematical formulation of the Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional relativistic effects such as time dilation would not apply as they would with conventional motion at near-light speeds.

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ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j

1 $ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Empty$ ds^2 = -left(alpha^2- beta_i beta^iright),dt^2+2 beta_i ,dx^i, dt+ gamma_{ij},dx^i,dx^j 7/26/2014, 2:19 am

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2 $ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Empty$ Re: ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j 7/26/2014, 9:01 pm

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ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j

1 ds^2 = -left(alpha^2- beta_i beta^iright),dt^2+2 beta_i ,dx^i, dt+ gamma_{ij},dx^i,dx^j 7/26/2014, 2:19 am

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2 Re: ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j 7/26/2014, 9:01 pm

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1 $ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Empty$ ds^2 = -left(alpha^2- beta_i beta^iright),dt^2+2 beta_i ,dx^i, dt+ gamma_{ij},dx^i,dx^j 7/26/2014, 2:19 am

2 $ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j Empty$ Re: ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j 7/26/2014, 9:01 pm