Is Papapetrou line element the same as cylindrical coordinates?

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SUMMARY

The Papapetrou line element describes axial symmetric stationary spacetimes, utilizing coordinates labeled as ρ, z, and φ. These coordinates are similar to cylindrical coordinates but are not identical due to the curvature of spacetime. In flat spacetime, the transformation to spherical or Cartesian coordinates aligns with conventional cylindrical coordinates. However, in curved spacetime, this transformation differs, emphasizing the importance of understanding the context of spacetime curvature.

PREREQUISITES
  • Understanding of Papapetrou line element in general relativity
  • Familiarity with cylindrical coordinates and their properties
  • Knowledge of spacetime curvature and its implications
  • Basic grasp of transformations between coordinate systems
NEXT STEPS
  • Research the properties of the Papapetrou line element in detail
  • Study the differences between curved and flat spacetime metrics
  • Learn about transformations between cylindrical, spherical, and Cartesian coordinates
  • Explore axial symmetry in general relativity and its applications
USEFUL FOR

Physicists, particularly those specializing in general relativity, students studying spacetime metrics, and researchers interested in the implications of axial symmetry in gravitational theories.

Saeide
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Hi all,

Papapetrou line element describes an axial symmetric stationary spacetimes and the coordinates that appear in this metric are just similar to cylindrical coordinates; I mean they are labeled ρ, z and phi. I want to know if they are really the cylindrical coordinate or not; In other words, are their transformation to spherical or cartesian coordinates the same as what we have in the literature?

So thanks in advance,

Saeide
 
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Saeide, The spacetime is curved, so I don't understand what you mean by "really" the cylindrical coordinates. At large distances where the spacetime becomes flat they tend to the usual Euclidean cylindrical coordinates.
 
Yes you're right. I forgot about the flat space limit.
 

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