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TimeRip496
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How do you obtain this equation M=Gm/c^2. What does M stand for? Is is Newton law at infinity? Again what is this Newton law at infinity?
TimeRip496 said:How do you obtain this equation M=Gm/c^2. What does M stand for?
Do you mind telling me a source for such derivation? Cause all the Internet gives is just the derivation of the schwarzschild radius.Nugatory said:M is just the mass of the black hole using units in which G and c are both equal to one.
We don't have to make this substitution but if we don't we'll be schlepping factors of G and c around everywhere in our equations, and they're complicated enough already.
TimeRip496 said:Do you mind telling me a source for such derivation?
The Schwarzschild metric is a mathematical formula in the field of general relativity that describes the curvature of spacetime around a non-rotating, spherically symmetric mass. It is named after the German physicist Karl Schwarzschild who first derived the metric in 1916.
The Schwarzschild metric is obtained by solving Einstein's field equations, which describe how matter and energy affect the curvature of spacetime. This involves using techniques from differential geometry and tensor calculus, and can be quite complex. The final result is the Schwarzschild metric, which is a solution to these equations for a static, spherically symmetric mass.
The equation M=Gm/c^2 is known as the Schwarzschild radius, and it is a key component of the Schwarzschild metric. It represents the distance from the center of a massive object at which the escape velocity would equal the speed of light. This means that anything within this radius, including light, would be unable to escape the strong gravitational pull of the object.
At large distances from a massive object, the Schwarzschild metric reduces to Newton's law of gravitation, which describes the gravitational force between two objects. This is known as the Newtonian limit of the Schwarzschild metric, and it shows that general relativity is consistent with Newton's theory of gravity in this regime.
The Schwarzschild metric has been used in various real-world applications, such as in the GPS system for accurately measuring time and position on Earth. It is also used in simulations of black holes and other astronomical objects, as well as in the study of gravitational lensing, which is the bending of light by massive objects in space.