The Spacetime Metric

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Classical and Quantum Gravity

Journal of gravitational physics and spacetime theory, published by IOP Publishing

Classical and Quantum Gravity publishes research on gravitation, relativity, cosmology and quantum gravity. Its warp-geometry papers include Alcubierre’s 1994 proposal, Bobrick and Martire’s 2021 analysis, and a 2024 constant-velocity subluminal solution. These papers examine mathematical models and their physical constraints; publication does not establish an experimentally demonstrated propulsion system.

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  • IOP Publishing

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Bibliography

A bibliography listing does not establish authorship. Credits appear under attribution.

Published bibliography entries: 3. Showing 1–3 of 3.

  1. Listed work

    Paper · 1994

    The warp drive: hyper-fast travel within general relativity

    1. Miguel Alcubierre(Author)

    Alcubierre’s 1994 paper specifies a mathematical geometry in which space expands behind a moving region and contracts ahead of it. A spacecraft at its center follows a freely falling path, remaining below the local speed of light even when distant observers assign it faster-than-light motion. In the prescribed geometry, its clock runs at the same rate as distant clocks during this central trajectory. Tidal forces near the spacecraft can be small for suitable size and shape parameters, while forces near the boundary can be large. Calculating the required matter and energy reveals negative energy density and violations of classical energy conditions. The paper invokes quantum examples such as the Casimir effect but supplies no method for producing the required distribution.

  2. Listed work

    Paper · 2021

    Introducing physical warp drives

    1. Alexey Bobrick(Author)
    2. Gianni Martire(Author)

    Bobrick and Martire model warp spacetimes as moving shells surrounding a flat passenger region, rather than as self-propelling engines. Their 2021 paper develops spherical configurations with positive energy at speeds below light, allowing gravity outside the shell and slower clocks inside relative to distant observers moving with it. They also explore changes to shape, interior volume and clock rates in other geometries. Flattening an Alcubierre configuration reduces its calculated negative-energy requirement, but the superluminal examples still violate the averaged null energy condition, a restriction on energy along light rays. Even their extremely thin examples that meet selected quantum inequalities retain this problem. Changing a shell’s velocity requires propulsion; a stationary geometry alone supplies no acceleration mechanism.

  3. Listed work

    Paper · 2024

    Constant Velocity Physical Warp Drive Solution

    1. Jared Fuchs(Author)
    2. Christopher Helmerich(Author)
    3. Alexey Bobrick(Author)
    4. Luke Sellers(Author)
    5. Brandon Melcher(Author)
    6. Gianni Martire(Author)

    Fuchs, Helmerich, Bobrick, Sellers, Melcher and Martire present a constant-velocity, slower-than-light warp drive solution that satisfies all of the energy conditions. It combines a stable shell of matter with a shift vector distribution closely matching well-known warp solutions such as the Alcubierre metric. The team generates the metric numerically, evaluates the energy conditions and confirms the shift cannot be removed by a change of coordinates. The result carries observers along geodesics, as the Alcubierre metric does, while satisfying the null, weak, dominant and strong energy conditions. Classic warp spacetimes can meet the energy conditions once a regular matter shell with positive ADM mass is added.