Basis Vector in GR: Cartesian Plane Comparisons

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SUMMARY

In the discussion regarding basis vectors in General Relativity (GR), it is established that while basis four vectors align with the x, y, z, and t coordinate axes, they do not share the same properties as Cartesian coordinates. Specifically, basis vectors in GR may lack orthonormality, meaning they can be non-perpendicular and of varying lengths. The text "Gravity: An Introduction to Einstein's General Relativity" by Hartle is deemed too advanced for some readers, suggesting that "Exploring Black Holes" may be a more suitable alternative for beginners.

PREREQUISITES
  • Understanding of General Relativity concepts
  • Familiarity with basis vectors and their properties
  • Knowledge of Cartesian coordinates and their characteristics
  • Basic grasp of orthonormality in vector spaces
NEXT STEPS
  • Study the properties of basis vectors in General Relativity
  • Learn about orthonormality and its implications in different coordinate systems
  • Read "Exploring Black Holes" for a more accessible introduction to GR
  • Examine the differences between Cartesian coordinates and curved spacetime coordinates
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Students and enthusiasts of General Relativity, educators seeking teaching materials, and anyone interested in the foundational concepts of spacetime and vector properties in physics.

Tony Stark
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I Have been reading hartle's book on Gr which states that basis four vectors point in x,y,z,t coordinate axes. So are they similar to the coordinate axis of Cartesian plane.
 
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Tony Stark said:
are they similar to the coordinate axis of Cartesian plane

Only in the very general sense that basis vectors point along coordinate axes. Coordinates in GR in general will not have many of the special properties that Cartesian coordinates on a plane have: a big one is that the basis vectors may not be orthonormal (which means the coordinate axes may not be perpendicular, and the lengths of the basis vectors may not all be the same).
 
I'm getting the sense that Hartle may be too advanced a text for the OP. Perhaps something like "Exploring black holes" would be a better choice.
 

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