Computing Lagrangian for Light Propagation in Spacetime

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SUMMARY

The Lagrangian for light propagation in curved spacetime is computed using an affine parameter instead of proper time, which is used for massive objects. This distinction is crucial for accurately determining the action for null curves. Understanding this concept is essential for anyone studying general relativity or related fields.

PREREQUISITES
  • General relativity fundamentals
  • Understanding of Lagrangian mechanics
  • Familiarity with affine parameters
  • Knowledge of null curves in spacetime
NEXT STEPS
  • Study the derivation of the Lagrangian for light in curved spacetime
  • Explore the concept of affine parameters in detail
  • Learn about null geodesics and their significance in general relativity
  • Investigate the action principle in the context of relativistic physics
USEFUL FOR

Students and researchers in physics, particularly those focusing on general relativity, theoretical physics, and anyone interested in the mathematical formulation of light propagation in spacetime.

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Does anyone know the Lagrangian for the propagation of light in curved spacetime? I'm disappointed to discover that I don't actually know how to compute the action for a given null curve.
 
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It's the same as for a massive object except instead of the proper time being your parameterization, you have to use just some random affine parameter.
 

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