User:Gpascu/Books/Mathematical Basis of General Relativity

Mathematical Basis of General Relativity

 * 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