Warp drive with zero expansion

In the zero-expansion warp bubble, the NEC, SEC, WEC, and DEC are all explicitly violated.

“In this situation explicit computation shows that the NEC, and so the SEC, WEC and DEC, are all explicitly violated.See specifically the original discussion in [2], and subsequent follow-up discussions in [14][15][16][17], and [20].”

Natario presents a general argument that in any generic warp spacetime, including Alcubierre, Natario zero-expansion, and Lentz/Fell-Heisenberg zero-vorticity, there must be violations of either the SEC or the WEC, or the trivial case of Minkowski space.

“note that in reference [10] Nat´ ario presents a quite general argument to the effect that in any generic warp spacetime, (Alcubierre, Nat´ ario zero-expansion, and, yes, it even applies to Lentz/Fell-Heisenberg zero-vorticity warp drives), there must be violations of either the SEC or the WEC. (Or you have the trivial case of Minkowski space.) See his theorem 1.7.”

The non-unit-lapse and van den Broeck warp drive spacetimes are physically different from the Natário class (unit lapse, spatially flat 3-geometry).

“There are other problematic issues with both of these models, but they are physically different from the Nat´ ario class [10], (unit lapse, spatially flat 3-geometry), and must be directly addressed using different techniques.”

The multi-compartment structure is a distinct departure from the single top-hat soliton found in [1] and [11].

“The multi-compartment structure is a distinct departure from the single top-hat soliton fond in [1] and [11].”

The Natário generic warp bubbles all have line elements of the form ds^2 = -dt^2 + δ_ij (dx^i - v^i(t,x)dt)(dx^j - v^j(t,x)dt).

“The Natário generic warp bubbles all have line elements explicitly of the form [2]:”

For the zero-expansion warp bubble, the flow field is solenoidal (divergence free).

“For the zero-expansion warp bubble the flow field v(t, x) is taken to be solenoidal (divergence free).That is ∇• v(t, x) = 0.”

Generic Natário warp drives have been shown to violate either the strong energy condition (SEC) or the WEC.

“and have also been shown to violate either the strong energy condition (SEC) or the WEC [10].”

Natário zero-expansion warp drives have long been known to violate the WEC.

“Nat´ ario zero-expansion warp drives have long been known to violate the WEC [10].”

The generic Natário line element covers all three specific cases (Alcubierre, Natário zero-expansion, Lentz/Fell-Heisenberg zero-vorticity) and many more, and is sufficiently general to cover almost all of the relevant literature.

“Thus the generic warp drive line element (2.1), introduced by Nat´ ario in [10], covers all three of these specific cases, and many more, and is sufficiently general to cover almost all of the relevant literature.”

All members of the general class of warp drives defined by Natario violate the NEC.

“We have now demonstrated that all members of the general class of warp drives defined by Nat´ ario [10] violate the NEC.”

The Natario zero-expansion warp drive definitely violates the WEC.

“So the Nat´ ario zero-expansion warp drive definitely violates the WEC [10].”

The argument applies to Alcubierre, Natario zero-expansion, Lentz/Fell-Heisenberg zero-vorticity warp drives, and also to the model warp drives considered by Bobrick-Martire.

“This argument applies, in particular, to all three of the Alcubierre [9], Nat´ ario zeroexpansion [10], and Lentz/Fell-Heisenberg zero-vorticity [1, 3] warp drives, and also (for slightly different reasons) to the model warp drives considered by Bobrick-Martire [2].”

There are two somewhat more general warp drive spacetimes that do not fall into Natario's general classification and are incompatible with the Alcubierre, Natario, and Lentz/Fell-Heisenberg warp drives.

“There are two somewhat more general warp drive spacetimes that do not fall into Nat´ ario's general classification [10], and are incompatible with the Alcubierre, Nat´ ario, and Lentz/Fell-Heisenberg warp drives.”

Natario has shown that expansion is not a fundamental feature of warp drives.

“However, Natario has shown that expansion is not a fundamental feature of warp drives [13].”