Find Null Geodesics with affine parameter

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SUMMARY

The discussion centers on finding null geodesics using an affine parameter in a specific metric context. The user is tasked with demonstrating that the null geodesics originating from r=0 and t=0 are defined by a particular equation. Despite providing an attempt at the solution, the user encounters a discrepancy in the sign of the result for t. The need for clearer image uploads is emphasized to facilitate assistance from other forum members.

PREREQUISITES
  • Understanding of null geodesics in differential geometry
  • Familiarity with affine parameters in the context of general relativity
  • Basic knowledge of metric tensors and their properties
  • Proficiency in LaTeX for mathematical expressions
NEXT STEPS
  • Study the derivation of null geodesics in general relativity
  • Learn about affine parameters and their role in geodesic equations
  • Explore the properties of metric tensors in curved spacetime
  • Practice using LaTeX for formatting mathematical equations
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on general relativity and differential geometry, will benefit from this discussion.

myra2016
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Homework Statement


The metric is given by
https://dl.dropboxusercontent.com/u/86990331/metric12334.jpg
H is constant; s is an affine parameter, and so r(0)=t(0)=0.

Apologise in advance because I'm not very good with LaTex. So I used Word for equations, and upload handwritten attempt at solution :smile:

Homework Equations


Need to show that the null geodesics from r=0, t=0 are given by
https://dl.dropboxusercontent.com/u/86990331/metricquestion.jpg

The Attempt at a Solution


I get the required t but the sign is different.
https://dl.dropboxusercontent.com/u/86990331/metricattemptatsolution.jpg
 
Last edited by a moderator:
Hello, please attempt to re-upload the images, currently the links appear to be broken and may very well be the reason no one can help.
 

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