# Changes between Initial Version and Version 28 of Ticket #26355

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Timestamp:
10/04/19 17:51:33 (2 years ago)
Comment:

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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 (M,g). Then the normal bundle T^\perp H intersect the tangent bundle TH. The radical distribution is defined as 'Rad(TH)=TH\cap T^\perp H'. In case of hypersurfaces, and more Rad(TH)=TH\cap T^\perp H. In case of hypersurfaces, and more generally 1-lightlike submanifolds, this is a rank 1 distribution. A screen distribution S(TH) is a complementary of Rad(TH) in TH. N = \frac{1}{g(\xi, v)}\left(v-\frac{g(v,v)}{2g(xi, v)}\xi\right) Tensors on the ambient manifold 'M' are projected on 'H' along 'N' Tensors on the ambient manifold M are projected on H along N to obtain induced objects. For instance, induced connection is the linear connexion defined on H through the Levi-Civitta connection of 'g' along N. linear connexion defined on H through the Levi-Civitta connection of g along N. To work on a degenerate submanifold, after defining H as an instance of :class:~sage.manifolds.differentiable.manifold.DifferentiableManifold, with the keyword *structure='degenerate'*, you have to set a transvervector v and screen distribution together with the radical distribution. with the keyword *structure='degenerate_metric'*, you have to set a transvervector v and screen distribution together with the radical distribution. An example of degenerate submanifold from General Relativity is the horizon of the Shawrzschild black hole. Allow us to recall that Shawrzschild 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:: horizon of the Schwarzschild black hole. Allow us to recall that Schwarzschild 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::