Question on Schwarzschild Geometry

In summary, the conversation discusses a specific radius, known as the Schwarzschild radius, which is determined by a given equation and is used to calculate the mass and density of stars and planets. The formula for calculating the radius involves a constant and the mass of the object. The conversation also addresses the issue of incorrect units being used in the calculations.
  • #1
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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  • #2
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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  • #3
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.
 
  • #4
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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  • #5
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.
 

Related to Question on Schwarzschild Geometry

1. What is Schwarzschild geometry?

Schwarzschild geometry is a mathematical model used to describe the curvature of space and time around a non-rotating, spherically symmetric mass, such as a black hole. It is named after the German physicist Karl Schwarzschild, who first derived the equations in 1916.

2. How does Schwarzschild geometry differ from Euclidean geometry?

Schwarzschild geometry is a non-Euclidean geometry, meaning it does not follow the rules of Euclidean geometry commonly used in everyday life. In Schwarzschild geometry, the curvature of space and time is affected by the presence of massive objects, while in Euclidean geometry, space and time are considered flat and do not change.

3. What is the event horizon in Schwarzschild geometry?

The event horizon in Schwarzschild geometry is the boundary around a black hole where the escape velocity is equal to the speed of light. This means that anything that crosses the event horizon, including light, cannot escape the gravitational pull of the black hole.

4. How does the Schwarzschild radius relate to black holes?

The Schwarzschild radius is a measure of the size of the event horizon of a black hole, and it is directly proportional to the mass of the black hole. This means that the more massive a black hole is, the larger its event horizon (and therefore, its Schwarzschild radius) will be.

5. How does general relativity explain gravity in the context of Schwarzschild geometry?

In general relativity, gravity is explained as the curvature of space and time caused by the presence of massive objects. In Schwarzschild geometry, this curvature is described by the Schwarzschild metric, which shows how the curvature of space and time changes with distance from the massive object. This explains how objects are attracted to each other even without an apparent force, as their paths are curved by the curvature of space and time.

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