Equations of motion in curved space

General Relativity (Fall, 2008)

Lecture Playlist

  1. Newtonian Gravity and the equivalence principle

  2. Tidal forces and curvature

  3. Essential tools: tensors and the metric

  4. Tensor mechanics

  5. Covariant differentiation and geodesics

  6. The flat space of special relativity

  7. The Riemannian curvature tensor

  8. Equations of motion in curved space

  9. Gravitation in the Newtonian approximation

  10. Energy-momentum tensor and Einstein's equations

  11. Accelerated coordinates

  12. World lines and Schwarzschild solution

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.

Topics: 
  • Covariant derivative
  • Riemann tensor
  • Newtonian approximation
  • Tangent vector
  • Curvature
References