Undergrad Why are contravariant and covariant vectors important in general relativity?

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SUMMARY

Contravariant and covariant vectors are fundamental in general relativity (GR) due to their roles in transforming between different coordinate systems. Contravariant vectors represent changes in displacement, while covariant vectors, akin to gradients, represent changes in functions such as curvature. These two independent vector spaces interact to produce Kronecker deltas, which are essential for calculations in GR. Understanding their physical significance enhances comprehension of the geometric nature of spacetime.

PREREQUISITES
  • Understanding of vector spaces and their properties
  • Familiarity with general relativity concepts
  • Knowledge of tensor calculus
  • Basic understanding of differential geometry
NEXT STEPS
  • Study the role of tensors in general relativity
  • Explore the mathematical foundations of differential geometry
  • Learn about the implications of Kronecker deltas in tensor operations
  • Investigate the physical interpretations of curvature in spacetime
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Students and professionals in physics, particularly those focusing on general relativity, theoretical physicists, and mathematicians interested in the geometric aspects of spacetime.

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1) I read different texts on Contravariant , Covariant vectors.
2) Contravariant - they say is like vector . Covariant is like gradient
From what I see they have those vector spaces because it eventually helps get scalar out of it if we multiply contravariant by covariant

Also Contravariant like chaneg in displacement and covariant is like change in function (may be the curvature of space here)

Is that right?

i understand contra/co are like 2 independent vector spaces and they act on each other to produce kronecker deltas but i fail to see why GR uses it so heavily and any physical meaning other than what i mentioned above

Thank You
 
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Thanks man
I have read a lot about contra covariant but most texts articles I read fail to provide motivation behind the same.
I was looking for that
I will read article you shared anyways
 

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