Gravitational time dilation on cylinderical objects

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SUMMARY

The discussion focuses on calculating gravitational time dilation for cylindrical objects with uniform density. Participants clarify the need for either an exact solution of the Einstein field equations or a weak-field approximation. The use of an arbitrary precision calculator, specifically the command line tool from http://pari.math.u-bordeaux.fr/, is recommended for advanced calculations. The conversation emphasizes the importance of defining the problem clearly to proceed with accurate calculations.

PREREQUISITES
  • Understanding of Einstein's field equations
  • Familiarity with gravitational time dilation concepts
  • Knowledge of integration techniques for potential calculation
  • Experience with command line tools for mathematical computation
NEXT STEPS
  • Research the exact solutions of Einstein's field equations for cylindrical symmetry
  • Study gravitational time dilation in weak-field approximations
  • Learn integration techniques for calculating gravitational potential
  • Explore the features of the PARI/GP arbitrary precision calculator
USEFUL FOR

Physicists, mathematicians, and students interested in gravitational physics, particularly those focusing on time dilation effects in cylindrical geometries.

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I am simply looking for the formula to work out the time dilation on cylinders with uniform density. Also, any links to arbitrary precision calculators would be appreciated.
 
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For the arbitrary precision calculator you could try http://pari.math.u-bordeaux.fr/
I have used it the past and it has some very advanced features, but you have to install it and it is a command line calculator.
 
Are you asking for (1) the time dilation resulting from an exact solution of the Einstein field equations, or (2) the time dilation in the weak-field limit, where the field is essentially Newtonian?

If it's 1, then I don't think you've specified enough to fully define the problem.

If it's 2, then you just need to calculate the potential of the cylinder by integrating. If you don't know how to do that, please tell us more about your math and science background, and we can try to help you at the correct level.

-Ben
 

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