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General formalism, classification, and demystification of the current warp-drive spacetimes

Hamed Barzegar, Thomas Buchert, Quentin Vigneron

Abstract

We critically examine proposals for the so-called warp-drive spacetimes and classify these models based on their various restrictions within the framework of General Relativity. We then provide a summary of general formalism for each class, and in the process, we highlight some misconceptions, misunderstandings, and errors in the literature that have been used to support claims about the physicality and feasibility of these models. On the way, we prove several new no-go theorems. Our analysis shows that when the principles of General Relativity are applied correctly, most claims regarding physical warp drives must be reassessed, and it becomes highly challenging to justify or support the viability of such models, not merely due to the violation of energy conditions.

General formalism, classification, and demystification of the current warp-drive spacetimes

Abstract

We critically examine proposals for the so-called warp-drive spacetimes and classify these models based on their various restrictions within the framework of General Relativity. We then provide a summary of general formalism for each class, and in the process, we highlight some misconceptions, misunderstandings, and errors in the literature that have been used to support claims about the physicality and feasibility of these models. On the way, we prove several new no-go theorems. Our analysis shows that when the principles of General Relativity are applied correctly, most claims regarding physical warp drives must be reassessed, and it becomes highly challenging to justify or support the viability of such models, not merely due to the violation of energy conditions.
Paper Structure (43 sections, 13 theorems, 123 equations, 1 figure)

This paper contains 43 sections, 13 theorems, 123 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notations
  3. General formalism and restrictions
  4. Foliations, metric and the geometry of motion
  5. Kinematics and dynamics of the fluid
  6. The matter model and energy-momentum conservation equations
  7. Conservation of energy and momentum in fluid rest frames
  8. Conservation of energy and momentum in Eulerian rest frames
  9. Rest mass, its density and conservation
  10. The 3+1 Einstein equations
  11. Principal scalar invariants of the second fundamental form
  12. Classification of warp-drive spacetimes
  13. Restrictions imposed on current warp-drive spacetimes
  14. Flow-orthogonal spacetimes (S-Warp models)
  15. Spatially conformally flat slices with generic shift vector and lapse function
  16. ...and 28 more sections

Key Result

Lemma 2.4

The expansion tensor and the second fundamental form in the tilted case are related to each other by the following equation: with $\mathfrak{a}_\mu$ from eq:naccel.

Figures (1)

  • Figure 1: The hierarchy of the pointwise energy conditions with implications depicted by arrows

Theorems & Definitions (68)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Lemma 2.4
  • Remark 2.5
  • Definition 3.1: Warp bubble
  • Remark 3.2
  • Definition 3.3: R-Warp model
  • Remark 3.4
  • Remark 3.5
  • ...and 58 more