Energy Density of the gravitational field

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SUMMARY

The discussion centers on the challenges of defining the energy density of a gravitational field, emphasizing the reliance on global energy concepts due to the equivalence principle. Participants highlight that any local measurement of gravitational energy density is dependent on the observer's coordinates, making it inherently ambiguous. Unlike electromagnetic fields, which have a well-defined energy density, gravitational fields do not possess a similar framework, complicating theoretical understanding. The Positive Energy Theorem is referenced as a key concept in this context, but existing literature fails to clarify these foundational issues.

PREREQUISITES
  • Understanding of the equivalence principle in general relativity
  • Familiarity with the Positive Energy Theorem
  • Knowledge of Lorentz transformations
  • Basic concepts of gravitational and electromagnetic fields
NEXT STEPS
  • Research the Positive Energy Theorem in detail
  • Study the implications of the equivalence principle on energy measurements
  • Explore Lorentz transformations and their effects on gravitational fields
  • Investigate the differences between gravitational and electromagnetic field energy densities
USEFUL FOR

The discussion is beneficial for physicists, students of general relativity, and researchers exploring the complexities of gravitational fields and their energy properties.

Geometrick
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Why is there no satisfactory way to define the energy density of a gravitational field? Why must we use global energy concepts? I'm currently reading proofs of the Positive Energy Theorem, but none of the references explains why this is so. Can anyone explain it or point me to a good reference?
 
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Because such an expression would depend on your coordinates due to the equivalence principle. If I measure a graviational field and say it has energy density in point x, then you can Lorentz-transform yourself to an accelerating observer and say that there is no gravitational field, so the energy density is 0.

This is completely different from, let's say, the electromagnetic field.
 

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