Schwarzschild Radius Derivation: Is it Possible Classically?

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SUMMARY

The discussion centers on the classical derivation of the Schwarzschild radius, defined as r = GM/c², using Newtonian gravity principles without resorting to Einstein's field equations. Participants confirm that by setting the escape velocity equal to the speed of light (c), one can derive the radius as r = 2GM/c². However, they emphasize that the interpretation of this radius differs significantly between Newtonian gravity and General Relativity (GR).

PREREQUISITES
  • Understanding of Newtonian gravity principles
  • Familiarity with escape velocity calculations
  • Basic knowledge of General Relativity concepts
  • Mathematical proficiency in algebra and calculus
NEXT STEPS
  • Research the implications of escape velocity in General Relativity
  • Study the differences between Newtonian gravity and General Relativity
  • Explore the derivation of the Schwarzschild solution in GR
  • Learn about the physical significance of the Schwarzschild radius
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Physicists, students of theoretical physics, and anyone interested in the foundations of gravitational theory and the transition from classical to modern physics.

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Is it possible to derive r=GM/c^2 classically(as in Newtonian gravity) without using eeinstein field equation?
 
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You can set the escape velocity to ##c## and find this radius immediately in Newtonian gravity: ##c=\sqrt{\frac{2GM}{r}}\rightarrow ~r=\frac{2GM}{c^2}## however, what this radius means in Newtonian gravity is not the same as what it means in GR.
 

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