Question on Schwarzschild Geometry

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Discussion Overview

The discussion revolves around the interpretation of the Schwarzschild radius in relation to the mass and density of celestial bodies, specifically focusing on the mathematical relationships and units involved in these calculations. Participants explore theoretical implications and mathematical formulations associated with the Schwarzschild geometry.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a formula relating the Schwarzschild radius to the mass and density of celestial bodies, suggesting a specific radius that yields correct mass values.
  • Another participant points out that the relationship presented involves a division by a constant, which leads to a mass result, but notes that the units used are incorrect, highlighting that a radius times a volume does not equate to mass.
  • A different participant proposes an equation for the Schwarzschild radius, asserting that dividing mass by the Schwarzschild radius yields a constant value, which they equate to a specific numerical expression involving volume.
  • One participant challenges the dimensional consistency of the equations presented, arguing that the units do not align correctly, comparing it to a nonsensical statement about weight and speed.
  • A later reply acknowledges the previous critique about units and attempts to clarify the relationship between mass and the Schwarzschild radius, suggesting a specific mass per unit length of the Schwarzschild radius.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correctness of the units and the mathematical relationships presented. There is no consensus on the validity of the initial claims or the interpretations of the Schwarzschild radius in this context.

Contextual Notes

Participants highlight limitations related to unit consistency and dimensional analysis, indicating that some mathematical steps may be unresolved or misinterpreted.

nabil23
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please interpret this observation. There is a specific radius through a given equation that always gives the correct mass to any star or planet, as well a density. What is the logical explanation for this?
Mass = (4π/3) x schwarzschild radius of the star x 4π/3 x (726696460.5 cm.) cube.
For example Earth mass is equal to:

M= 4.188786667 x 0.8870085587 cm. x 4.188786667 x (726696460.5 cm.) cube = 5.9726 x (10) +27 gram.

(4π/3) = 4.188786667
schwarzschild radius of the Earth = 0.8870085587 cm.
the mentioned radius = 726696460.5 cm.
the density of Earth is equal to:
earth density ρ= M/V = (4π/3) x 0.8870085587 cm. x (4π/3) x (726696460.5 cm) cube /(4π/3) x (637758965.3 cm) cube = Earth density.
the radius of the Earth = 637758965.3 cm.
thank you for your contribution and your effort in providing explanation.
 
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The Schwarzschild radius is the mass multiplied by a constant. You've divided by that constant (or multiplied by its reciprocal). Unsurprisingly, the result is the mass.

Edit: Well, numerically at least. Your units are messed up - a radius times a volume is not a mass.
 
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I think that schwarzschild radius is equal to:
schwarzschild radius = M/(C x C/2G) = M/6.733418682 x (10) +27
any mass divided on schwarzschild radius will give this constant:
M/schwarzschild radius = 6.733418682 x (10) +27
this constant is actually equal to :
(4π/3) x (4π/3) x (726696460.5 cm.) cube = 6.733418682 x (10) +27
c= 29979245800 cm. speed of light in centimeter/second.
726696460.5 is the mentioned radius mentioned above.
 
You've still got messed up units. ##G/c^2## has dimensions of ##LM^{-1}## (units of cm/kg, in the system you are using). This cannot be meaningfully equal to a radius cubed. It's like saying I weigh 70 miles per hour. It's nonsense - I weigh 70kg. The numbers are the same but the meaning is totally different.
 
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you are absolutely right :
Mass/ schwarzschild radius = M/rs = c x c/2G = ML-1 = 6.733418682 x (10) +27 gram/centimeter
it means 6.733418682 x (10)+27 gram for every 1 centimeter of schwarzschild radius length.
 

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