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blue_sky
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Where can I found the rigorous Schwarzschild solution INSIDE a body?
blue_sky said:Where can I found the rigorous Schwarzschild solution INSIDE a body?
Its not called the Schwarzschild solution, but the derivation of the weak field solution for steller interiors is touched on in MTW's Gravitation. More generally the following works:blue_sky said:Where can I found the rigorous Schwarzschild solution INSIDE a body?
jcsd said:I think he's talking about the solution inside spherically symmetric objects of constant density, at least that's how I read it.
I just gave it to you. The solution is consistent with an ideal gass. Aside from "Modern Relativity" the web site, good luck finding the the case for arbitrary density anywhere.blue_sky said:Yup, you right but not costant density; I'm looking for the solution inside spherically symmetric objects with density following the rules of a perfect gas.
in particular I'm looking for p=p(r) in that case.
blue
blue_sky said:Where can I found the rigorous Schwarzschild solution INSIDE a body?
blue_sky said:I'm looking for the solution inside spherically symmetric objects with density following the rules of a perfect gas, in particular I'm looking for p=p(r) in that case.
The Schwarzschild Solution is a mathematical solution to Einstein's field equations that describe the curvature of spacetime in the presence of a non-rotating, spherically symmetric mass. It is named after German physicist Karl Schwarzschild who first derived this solution in 1916.
The solution involves two key components: the Schwarzschild radius, which marks the boundary of the event horizon of a black hole, and the Schwarzschild metric, which describes the curvature of spacetime around the black hole. The metric takes into account the mass of the black hole and the distance from its center.
The rigorous inside body refers to the region inside the event horizon of a black hole, where the gravitational pull is so strong that even light cannot escape. The Schwarzschild Solution allows us to better understand the properties and behavior of black holes, which are some of the most extreme and mysterious objects in the universe.
Yes, the Schwarzschild Solution can also be applied to other massive, spherically symmetric objects such as stars. In fact, the Schwarzschild metric is used in astrophysics to model the gravitational field of stars and other celestial bodies.
One limitation of the Schwarzschild Solution is that it assumes a static, non-rotating mass. In reality, most astronomical objects are rotating and have other complexities that cannot be fully described by this solution. Additionally, the Schwarzschild Solution does not take into account quantum effects, which are important at the scale of black holes.