Equations of motion in curved space

General Relativity (Fall, 2008)

November 10, 2008

Define the covariant derivative.

Define the Riemann curvature tensor through the commutation of the covariant derivative.

Two types of curvature are intrinsic and extrinsic

Determine the equation of motion given by the covariant derivative of the tangent vector.

Find the Newtonian approximation to the Einstein tensor.

  • Covariant derivative
  • Riemann tensor
  • Newtonian approximation
  • Tangent vector
  • Curvature