L = 0 in the equation for effective potential energy?

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SUMMARY

Setting angular momentum (L) to zero in the context of effective potential energy leads to a scenario of radial infall. In General Relativity (GR), this corresponds to a test particle moving in a Schwarzschild spacetime. Understanding this concept requires a solid grasp of the Kepler problem in Newtonian physics, where solutions can be derived using standard elementary functions. This foundational knowledge simplifies the transition to more complex GR treatments.

PREREQUISITES
  • Understanding of angular momentum in physics
  • Familiarity with the Kepler problem in Newtonian physics
  • Basic knowledge of General Relativity concepts
  • Comprehension of Schwarzschild spacetime
NEXT STEPS
  • Study the Kepler problem in Newtonian physics
  • Learn about angular momentum and its implications in gravitational systems
  • Explore the concept of effective potential energy in both Newtonian and General Relativity contexts
  • Investigate the dynamics of test particles in Schwarzschild spacetime
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Students and researchers in physics, particularly those focusing on gravitational dynamics, General Relativity, and classical mechanics.

sqljunkey
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Hi,

What would happen if I set L in this equation to zero? I can have an L that is zero right?
 
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Sure. That would be zero angular momentum. What do you expect to happen?

(EDIT: Which equation, exactly? There are many on that page.)
 
L can be zero. From context, L is just the angular momentum, and L=0 corresponds to a radial infall. This is the GR forum, so I'd guess you are most likely interested in the GR case, though it's possible you are interested in the Newtonian case as well.
 
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Start with a thorough study of the Kepler problem in Newtonian physics. There (almost) everything can be solved in analytical form with standard elementary functions. After that it's easier to understand the general-relativsitic treatment (test particle in a Schwarzschild spacetime).
 

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