Basic notions

 

• Riemann geometry, metric tensor , covariant components

  
  
  

• contravariant components of metric tensor

  
  
  

• Christoffel symbols of the first kind

  
  
  

• Christoffel symbols of the second kind

  
  
  

• Riemann curvature tensor

  
  
  

• Ricci tensor

  
  
  

• for a general metric in 4D, there are 9 990 diagonal and 13 280 off-diagonal terms

• Ricci scalar

  
  
  

• Einstein vacuum equations

  
  
  

• system of second order nonlinear partial differential equations with cosmological constant