From SR to GR in an easy math (and physical) way

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SUMMARY

The discussion focuses on transitioning from Special Relativity (SR) to General Relativity (GR) using differential geometry. The user inquires about a simplified method to derive the Einstein field equations, specifically asking if the condition \(\nabla_{u} u=0\) can lead to \(\nabla R_{ab} =0\) without relying on Lagrangian formalism. The conversation emphasizes the need for clarity in understanding the mathematical framework that connects these two theories, particularly in the context of geodesics and the evolution of the universe.

PREREQUISITES
  • Understanding of Special Relativity (SR) principles
  • Familiarity with General Relativity (GR) concepts
  • Knowledge of differential geometry
  • Basic grasp of the Einstein field equations
NEXT STEPS
  • Research the derivation of the Einstein field equations from differential geometry
  • Study the relationship between geodesics and the curvature of spacetime
  • Explore Lagrangian formalism in the context of General Relativity
  • Learn about the implications of \(\nabla R_{ab} =0\) in gravitational theories
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Physicists, mathematicians, and students of theoretical physics interested in the mathematical foundations of General Relativity and its relationship to Special Relativity.

lokofer
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From SR to GR in an "easy" math (and physical) way

Hello..i know that for example to go from Newtonian to SR you take:

[tex]\frac{du}{ds}=0 \rightarrow \nabla _{u} u=0[/tex]

My question is ¿is there an "easy" form to go from SR to GR in the form:

[tex]\nabla _{u} u=0 \rightarrow \nabla R_{ab} =0[/tex]
Or to get Einstein equation appart from using the Lagrangian formalism... using "Differential Geomertry" or similar...:confused: :confused:
 
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Your first claim doesn't make much sense to me. Can you clarify?
Are you trying to describe the evolution of the universe as a geodesic in some abstract space?
 

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