Schwarzschild black hole with cosmological constant

What we do?

Schwarzschild black hole with cosmological constant is 4-dimentional Lorentz manifold with constant Ricci curvature, timelike Killing vector field and group SO(3) as a subgroup of the manifold isometry group (with spacelike orbits).
For Schwarzschild metric calculate the following:
  • connetion 1-forms
  • curvature 2-forms
  • Riemannin tensor field
    • Ricci tensor field
    Verify that are Killing vector vields.

Solution:

Domain[manifold]manifold - string - a manifold name or a name of a manifold domain.
Metric[id→expr]id - variable - metric identifier, expr - expression - metric declaration.
Connection[id]id - variable - connection identifier.

Necessary functions.

Load the Atlas package:
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Schwarzschild metric

Constants:
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Vector fields:
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Differential p-forms:
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Coframe 1-forms:
Frame vector fields:
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Metric tensor field:
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Connection 1-forms:
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Curvature 2-forms:
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Curvature tensor field:
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Ricci tensor field calculation:
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Verify that metric g is Einstein one:
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Verify that and are Killing vector fields:
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