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  2. Alcubierre drive - Wikipedia

    en.wikipedia.org/wiki/Alcubierre_drive

    The Alcubierre metric defines the warp-drive spacetime.It is a Lorentzian manifold that, if interpreted in the context of general relativity, allows a warp bubble to appear in previously flat spacetime and move away at effectively faster-than-light speed.

  3. Christoffel symbols - Wikipedia

    en.wikipedia.org/wiki/Christoffel_symbols

    In general relativity, the connection plays the role of the gravitational force field with the corresponding gravitational potential being the metric tensor. When the coordinate system and the metric tensor share some symmetry, many of the Γ i jk are zero. The Christoffel symbols are named for Elwin Bruno Christoffel (1829–1900). [7]

  4. Cylindrical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cylindrical_coordinate_system

    A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane ...

  5. Born coordinates - Wikipedia

    en.wikipedia.org/wiki/Born_coordinates

    The Born coordinates are also sometimes referred to as rotating cylindrical coordinates. In the new chart, the world lines of the Langevin observers appear as vertical straight lines. Indeed, we can easily transform the four vector fields making up the Langevin frame into the new chart. We obtain

  6. Weyl–Lewis–Papapetrou coordinates - Wikipedia

    en.wikipedia.org/wiki/Weyl–Lewis–Papapetrou...

    In general relativity, the Weyl–Lewis–Papapetrou coordinates are used in solutions to the vacuum region surrounding an axisymmetric distribution of mass–energy. They are named for Hermann Weyl , Thomas Lewis, and Achilles Papapetrou .

  7. van Stockum dust - Wikipedia

    en.wikipedia.org/wiki/Van_Stockum_dust

    In general relativity, the van Stockum dust is an exact solution of the Einstein field equations where the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is increasing with distance from this axis, the solution is rather artificial, but as one of the simplest known ...

  8. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    is also a Riemannian metric on . We say that ~ is (pointwise) conformal to . Evidently, conformality of metrics is an equivalence relation. Here are some formulas for conformal changes in tensors associated with the metric.

  9. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.