Changes between Initial Version and Version 28 of Ticket #26355


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Timestamp:
10/04/19 17:51:33 (2 years ago)
Author:
Dicolevrai
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  • Ticket #26355

    • Property Status changed from new to needs_review
    • Property Cc Eric Gourgoulhon removed
    • Property Summary changed from Classes DegenerateManifold and DegenerateSubmanifold to Degenerate Metric and Degenerate Metric Manifold
    • Property Branch changed from public/manifolds/DegenerateSubmanifold to public/manifolds/DegenerateMetricManifold
    • Property Milestone changed from sage-8.4 to sage-8.9
    • Property Commit changed from b2523bbbf62de2e1c4a39fab1aa557f68d92e2cf to e9f8bba07c03da6e45bec04df721c115f4063959
  • Ticket #26355 – Description

    initial v28  
    2525`(M,g)`. Then the normal bundle `T^\perp H` intersect the tangent
    2626bundle `TH`. The radical distribution is defined as
    27 'Rad(TH)=TH\cap T^\perp H'. In case of hypersurfaces, and more
     27`Rad(TH)=TH\cap T^\perp H`. In case of hypersurfaces, and more
    2828generally `1-`lightlike submanifolds, this is a rank 1 distribution.
    2929A screen distribution `S(TH)` is a complementary of `Rad(TH)` in `TH`.
     
    3939    N = \frac{1}{g(\xi, v)}\left(v-\frac{g(v,v)}{2g(xi, v)}\xi\right)
    4040
    41 Tensors on the ambient manifold 'M' are projected on 'H' along 'N'
     41Tensors on the ambient manifold `M` are projected on `H` along `N`
    4242to obtain induced objects. For instance, induced connection is the
    43 linear connexion defined on H through the Levi-Civitta connection of
    44 'g' along `N`.
     43linear connexion defined on `H` through the Levi-Civitta connection of `g` along `N`.
    4544
    4645To work on a degenerate submanifold, after defining `H` as an instance
    4746of :class:`~sage.manifolds.differentiable.manifold.DifferentiableManifold`,
    48 with the keyword *structure='degenerate'*, you have to set a transvervector
    49 `v` and screen distribution together with the radical distribution.
     47with the keyword *structure='degenerate_metric'*, you have to set a transvervector `v` and screen distribution together with the radical distribution.
    5048
    5149An example of degenerate submanifold from General Relativity is the
    52 horizon of the Shawrzschild black hole. Allow us to recall that
    53 Shawrzschild black hole is the first non-trivial solution of Einstein's
    54 equations. It describes the metric inside a star of radius `R = 2m`,
    55 being `m` the inertial mass of the star. It can be seen as an open
    56 ball in a Lorentzian manifold structure on `\RR^4`::
     50horizon of the Schwarzschild black hole. Allow us to recall that
     51Schwarzschild black hole is the first non-trivial solution of Einstein's equations. It describes the metric inside a star of radius `R = 2m`, being `m` the inertial mass of the star. It can be seen as an open ball in a Lorentzian manifold structure on `\RR^4`::