Understanding Einstein-Hilbert Action: Detailed Explanation from an Expert

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SUMMARY

The Einstein-Hilbert action is the foundational principle in General Relativity (GR) that yields the field equations when variations with respect to the metric are set to zero. The action is derived from the Ricci scalar, which is the simplest and most general scalar that encodes the curvature of spacetime. This choice is significant as it involves the inverse metric and the Ricci tensor, encapsulating all necessary information for the field equations. Understanding this action is crucial for grasping the principles of variational mechanics in the context of GR.

PREREQUISITES
  • General Relativity (GR) fundamentals
  • Ricci scalar and Ricci tensor concepts
  • Variational mechanics principles
  • Metric tensor understanding
NEXT STEPS
  • Study the derivation of the Einstein field equations from the Einstein-Hilbert action
  • Explore the role of the Ricci scalar in curvature and spacetime geometry
  • Learn about variational principles in classical mechanics
  • Investigate the implications of the metric tensor in GR
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Students and researchers in physics, particularly those focusing on General Relativity, theoretical physicists, and anyone interested in the mathematical foundations of spacetime and gravity.

Terilien
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Can someone explain to me why this is the appropriate action?It makes some sens that that would be used, but I'd like a detailed explanation from someone familiar with the topic.

Why is it the one that yields the proper equations?
 
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Well, for a start, you can derive the field equations by setting variations of this action with respect to the metric equal to zero. This is done in many GR texts.
 
Yes but what is the intuition behind it? What lead hilbert to choose that particular action?
 
Can you think of a simpler scalar that encodes the curvature of spacetime? The Ricci scalar is a fairly obvious choice.
 
So essentially it used because its the simplest, most general(encodes curvature) involves the inverse metric, the ricci tensor, etc.. and such. So essentially its simple and encodes all the information that we may want tin the field equations...


This is the first time I've emcountered this topic(variational mechanics) so it seems quite exotic. Its very interesting though.

It would however be nice, to gain whatever insight I can into this principle and this topic in general.
 
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