Things that do not depend on the choice of Cauchy surface

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SUMMARY

The discussion centers on the concept of a Cauchy surface, defined as a 3D spacelike slice of spacetime. The author asserts that the properties of the functions on a Cauchy surface, denoted as ##\sigma##, are independent of the choice of the Cauchy surface due to adherence to the law of motion. Participants seek clarification on this proof and its implications, indicating a need for deeper understanding of the relationship between Cauchy surfaces and physical laws.

PREREQUISITES
  • Understanding of general relativity and spacetime concepts
  • Familiarity with the definition and properties of Cauchy surfaces
  • Knowledge of the law of motion in physics
  • Ability to interpret mathematical proofs in theoretical physics
NEXT STEPS
  • Study the mathematical framework of Cauchy surfaces in general relativity
  • Explore the implications of the law of motion on spacetime geometry
  • Review proofs related to the independence of physical laws from Cauchy surface choices
  • Investigate advanced topics in differential geometry relevant to spacetime analysis
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The discussion is beneficial for theoretical physicists, students of general relativity, and mathematicians interested in the geometric aspects of spacetime and Cauchy surfaces.

naima
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A Cauchy surface is a 3d spacelike slice of spacetime.
Could you read the definition (17) p18
the author says that "one can proove that ##\sigma## does not depend on the choice of the Cauchy surface because the functions obey the law of motion."
Could you elaborate?
Thanks

Could anyone add "h" in the title (choice)?
 
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I found the proof several lines below!
 

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