Tensors and Relativity: Chapter 8

The Schwarzschild Solution

The gravitational fields which are most important in our daily lives, namely that of the earth, moon and sun, are produced by slowly rotating, nearly spherical mass distributions, i.e. they are approximately spherically symmetric. Because of their importance we will try and solve Einstein's equations for such bodies.

• The line element
• The Christoffel symbols
• The Ricci Tensor
• The vacuum field equations
• The Schwarzschild solution
• General discussion of the Schwarzschild solution
  • Time dilation in a gravitational field
  • Length contraction in a gravitational field
• Orbits in Schwarzschild spacetime
  • Solution for timelike orbits and precession
  • The bending of light
• Index
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