User:Gpascu/Books/Mathematical Basis of General Relativity
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Mathematical Basis of General Relativity
[edit]- Introduction
- Mathematics of general relativity
- Diffeomorphism
- Differential Geometry Notions
- Lie derivative
- Covariant derivative
- List of formulas in Riemannian geometry
- Christoffel symbols
- Relative scalar
- Tensors
- Tensor
- Abstract index notation
- Tensor contraction
- Contraction mapping
- Einstein notation
- Raising and lowering indices
- Symmetric tensor
- Antisymmetric tensor
- Dual
- Tensor density
- Pseudotensor
- Tensors in General Relativity
- Metric tensor (general relativity)
- Ricci curvature
- Riemann curvature tensor
- Torsion tensor
- Weyl tensor
- Plebanski tensor
- Stress–energy tensor
- Stress–energy–momentum pseudotensor
- Belinfante–Rosenfeld stress-energy tensor
- Cotton tensor
- Bach tensor
- Schouten tensor
- Einstein tensor
- Bel-Robinson tensor
- Lanczos tensor
- Electromagnetic tensor
- Ricci decomposition
- Bel decomposition
- Magnetogravitic tensor
- Electrogravitic tensor
- Topogravitic tensor
- Segre classification
- Petrov classification
- Symmetries in General Relativity
- Spacetime symmetries
- Killing vector field
- Homothetic vector field
- Affine vector field
- Projective vector field
- Conformal vector field
- Curvature collineation
- Matter collineation
- Killing tensor
- Invariants
- Curvature invariant
- Curvature invariant (general relativity)
- Scalar curvature
- Kretschmann scalar
- Carminati–McLenaghan invariants
- Cartan–Karlhede algorithm