Null Hyperplanes & Cauchy Surfaces in Spacetimes

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    Cauchy Surfaces
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SUMMARY

A null hyperplane is not a Cauchy surface in Minkowski spacetime, as clarified in the discussion. The concept of a Cauchy surface is defined in detail in Sean Carroll's book, "An Introduction to General Relativity: Spacetime Geometry," specifically on pages 79-80. The discussion raises questions about the status of null hyperplanes in other spacetimes, indicating that further exploration is necessary to understand their properties in those contexts.

PREREQUISITES
  • Understanding of Minkowski spacetime
  • Familiarity with Cauchy surfaces
  • Knowledge of general relativity concepts
  • Access to Sean Carroll's "An Introduction to General Relativity: Spacetime Geometry"
NEXT STEPS
  • Study the definition and properties of Cauchy surfaces in various spacetimes
  • Examine the implications of null hyperplanes in general relativity
  • Read Sean Carroll's book for a comprehensive understanding of spacetime geometry
  • Research the characteristics of other spacetimes beyond Minkowski
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Students and researchers in theoretical physics, particularly those focusing on general relativity and spacetime geometry.

paweld
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Is a null hyperplane a Cauchy surface in Minkowski spacetime?
What in case of other spacetimes?
 
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paweld said:
Is a null hyperplane a Cauchy surface in Minkowski spacetime?

This is something that you should try to work through. What is a Cauchy surface? A readable definition is given on pages 79-80 of Sean Carroll's book An Introduction to General Relativity: Spacetime Geometry. This is just one example of where Carroll's book is better than Carroll'a arXiv notes.
paweld said:
What in case of other spacetimes?

I am not sure what you're asking.
 

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