Metric for an observer in free fall two schwarzchild radii from black hole.

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SUMMARY

The discussion centers on finding the metric for an observer in free fall at a distance of two Schwarzschild radii (2rs) from a black hole. The participant seeks clarification on substituting r=2rs and dt=d(tau) into the Schwarzschild metric. They also inquire whether this scenario qualifies as a radial trajectory, allowing for the simplification of d(theta) and d(phi) to zero. The consensus is that these substitutions are valid for the metric calculation.

PREREQUISITES
  • Understanding of General Relativity (GR) principles
  • Familiarity with the Schwarzschild metric
  • Knowledge of proper time (tau) and coordinate time (t) relationships
  • Concept of radial trajectories in curved spacetime
NEXT STEPS
  • Study the derivation of the Schwarzschild metric in detail
  • Learn about proper time versus coordinate time in General Relativity
  • Explore the implications of radial trajectories in black hole physics
  • Investigate the effects of gravitational time dilation near black holes
USEFUL FOR

Students of General Relativity, physicists preparing for exams, and anyone interested in the mathematical modeling of black hole physics.

Sae_Phys
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Hi all,

I have a GR exam on tuesday and getting a bit confused as to how to find the metric for an observer in free fall a distance two schwarzchild radii from a black hole.

I know this is a bit of a basic question but I am just wondering if I am correct to substitute r=2rs and dt=d(tau) into the usual metric and simplify. Also does this class as a radial trajectory so can you set d(theta) and d(phi) =0 ... HELP!

Thanks :)
 
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