Definition of Inertial Frame in GR: Math Explained

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SUMMARY

An inertial frame in General Relativity (GR) is mathematically defined as a basis in the tangent space. It is not necessarily induced by a coordinate chart; however, local coordinates can be established that induce this basis at a single point. These specific local coordinates are referred to as normal coordinates, which facilitate the analysis of physical phenomena in the vicinity of that point.

PREREQUISITES
  • Understanding of General Relativity concepts
  • Familiarity with tangent spaces in differential geometry
  • Knowledge of coordinate systems and their applications
  • Basic grasp of normal coordinates in mathematical physics
NEXT STEPS
  • Study the mathematical framework of General Relativity
  • Explore the properties and applications of tangent spaces
  • Learn about normal coordinates and their significance in GR
  • Investigate the relationship between coordinate charts and physical laws in GR
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Students and researchers in theoretical physics, mathematicians specializing in differential geometry, and anyone interested in the mathematical foundations of General Relativity.

Kontilera
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How do we mathematically define a inertial frame in GR?
Is it only a basis in some tangentspace or does it have to be induced by a coordinatechart? :/
 
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It's only a basis in the tangent space. But you can always find local coordinates that induce this basis at a single point. They are called normal coordinates.
 

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