Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License.

  • noun Plural form of hypersurface.

Etymologies

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Examples

  • We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constant-density hypersurfaces in a Friedmann-Robertson-Walker cosmology.

    Ripples in the Aether

  • Your candidate should be able to quasi-exponentially expand the universe, flatten out its spatial hypersurfaces, causally connect seemingly unconnected regions of the microwave sky, generate all the matter content of later epochs (reheating) and imprint upon it the density perturbations necessary to seed our observed large scale structure.

    Constraints and Signatures in Particle Cosmology

  • We imagined that there were some hypothetical vector field that had a nonzero value in empty space, but which (basically) pointed along a timelike direction, orthogonal to hypersurfaces of constant cosmological time.

    Anatomy of a Paper: Part II, Calculation

  • Huisken was working on the Mean Curvature Flow for hypersurfaces,which closely parallels the Ricci Flow,being the most natural flows for intrinsic and extrinsic curvature respectively.

    Quick note: Yau vs New Yorker

  • One way to do this is by means of additional Lorentz invariant dynamical structure, for example a suitable time-like 4-vector field, that permits the definition of a foliation of space-time into space-like hypersurfaces providing a Lorentz invariant notion of "evolving configuration" and along which nonlocal effects are transmitted.

    Bohmian Mechanics

  • In Figure 1 the planes represent the hypersurfaces of simultaneity.

    Backward Causation

  • But neither with respect to the frame S* nor S** is the tachyon source at rest and the hypersurfaces are therefore tilted in relation to the arrow of trajectory.

    Backward Causation

  • Σ² Š‚ M² are spacelike hypersurfaces in hole-free spacetimes

    Time Machines

  • M² be spacelike hypersurfaces of their respective spacetimes.

    Time Machines

  • The spacetime structure that is implied by special relativity is thus an affine space, like Newtonian spacetime, but it is not objectively divided into hypersurfaces of absolute simultaneity; the sets of simultaneous events for any inertial frame are the hyperplanes orthogonal to the trajectories that determine that frame.

    Space and Time: Inertial Frames

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