The warp drive: hyper-fast travel within general relativity

In the citing paper

“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 [1], and the subsequent follow-up discussions in [12][13][14][15][16][17], and [20,21].”

In the citing paper

“For the Alcubierre warp bubble the flow field v(t, x) is auto-parallel. That is v(t, x) = v(t, x) v;v = (constant).”

In the citing paper

“The transport logistics of the presented positive-energy solitons are similar to the solitons of the Alcubierre solution.”

In the citing paper

“The solution of [1] possesses only one negative expansion lobe at the leading edge of its soliton and one positive expansion lobe at the trailing edge.”

In the citing paper

“The largest values of θ for the positive-energy soliton coincide with the sources of stress-energy density, in contrast to the solution of Ref. [1] where the energy density and expansion factor are maximally separated on the soliton boundary.”

In the citing paper

“Alcubierre warp drives have long been known to violate the WEC [9]”

In the citing paper

“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].”

In the citing paper

“Specifically, in Alcubierre's original article [9, equation (6)] the concrete realization of the shape function f ( r s ) he chooses, see equation (A.8), uses tanh functions and so does not have compact support. In this terminology, Alcubierre sets r inner = 0 and r outer = ∞ , which is certainly not a truncation.”

In the citing paper

“Alcubierre's solution allows for acceleration using a time-varying v s ( t ).”

In the citing paper

“Alcubierre's solution is a shift vector addition to an otherwise Minkowski spacetime.”

In the citing paper

“Thus, it is clear that all the characteristic warp drive features of this spacetime are sourced purely by the shift vector.”

In the citing paper

“In a seminal paper, Alcubierre also concluded that the warp metric would imply the violation of the energy conditions since it appeared that a negative energy density would be required for the creation of the warp bubble.”

In the citing paper

“The field equations of general relativity (GR) permit inertial observers to be transported at superluminal rates relative to distance observers.”

In the citing paper

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

In the citing paper

“The Einstein tensor components were calculated and it was noticed that negative energy density would be required to create the warp bubble, thus violating the weak and dominant energy conditions.”

In the citing paper

“In the original paper by M. Alcubierre the warp drive metric was established without solving the Einstein equations [1].”

In the citing paper

“The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities.”

In the citing paper

“Motivated by the fact that neither the original paper by Alcubierre, nor the subsequent ones cited above, did actually solve the Einstein equations using the warp drive metric, we proceed to investigate possible solutions for a dust particle energy momentum tensor [26].”

In the citing paper

“In Ref. [1] the Einstein equations were not solved, since the metric was merely guessed with a form function (see Eq. 2.8) that rules the warp bubble shape.”

In the citing paper

“So far the proposed solutions have been unphysical, requiring energy condition violations and large energy requirements.”

In the citing paper

“The first warp drive solutions developed by Alcubierre [1] and then further developed by Van Den Broeck [16] enabled passengers inside the warp bubble to move at arbitrary speeds but at the cost of both enormous energy density and unphysical stress-energy tensors using negative energy.”

In the citing paper

“The Alcubierre metric violates all energy conditions within the bubble region, as it necessitates negative energy density, as Alcubierre demonstrated. This fact is confirmed through the analysis conducted using Warp Factory.”

In the citing paper

“In line with the Star Trek conception of warp drives, the first warp solution from Alcubierre was constructed such that the passengers and external observers both experience the same passage of time (proper time).”

In the citing paper

“For example, Alcubierre has a flat passenger volume and a warp bubble whose spatial extent is determined by a shape parameter 9 .”

In the citing paper

“Alcubierre introduced the first general relativistic warp drive in 1994 [1].”