What is the equation for the Schwarzschild Radius and why is π not included?

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SUMMARY

The Schwarzschild Radius is defined by the equation \( R_s = \frac{2GM}{c^2} \), where \( G \) is the gravitational constant, \( M \) is the mass of the black hole, and \( c \) is the speed of light. The absence of π in this equation is due to the fact that the Schwarzschild Radius specifically describes a critical radius for black holes, rather than geometric properties like circumference or volume that involve π. Understanding this distinction clarifies why π does not appear in the formula despite the spherical nature of black holes.

PREREQUISITES
  • Basic understanding of general relativity
  • Familiarity with gravitational physics
  • Knowledge of the constants \( G \) and \( c \)
  • Concept of black hole formation and properties
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  • Study the derivation of the Schwarzschild solution in general relativity
  • Explore the implications of the Schwarzschild Radius on black hole physics
  • Learn about the geometry of black holes and their event horizons
  • Investigate the role of π in other equations related to spherical objects
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carcosachild
Hello :)
I had a question , i recently red a lot about black holes and i had a question about the Schwarzschild
Radius . How does that come that π is not in the equation ? The black hole is a sphere so instinctly one could think that Pi should be in the equations.. ?
P.S: I'm french and 16 so sorry for the eventuals faults :)
 
Physics news on Phys.org
In geometry, you start with radius r. π comes into get circumference, area, volume, etc.
 

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