lugita15 said:Where can I find an accessible proof of Buchdahl's theorem, which states that in general relativity GM/(c^2*R) must be less than 4/9?
Any help would be greatly appreciated.
Thank You in Advance.
Buchdahl's theorem is a mathematical proof that sets a limit on the amount of mass and pressure that can be contained within a finite spherical object without it collapsing into a black hole. It was first proposed by physicist Hans Buchdahl in 1959.
Buchdahl's theorem states that for a given radius, the maximum ratio of mass to radius that a spherical object can have without collapsing into a black hole is 4/9, or approximately 0.444. This means that the more mass a spherical object has, the smaller its radius must be in order to avoid collapsing into a black hole.
Buchdahl's theorem is derived using the equations of Einstein's general theory of relativity. It involves solving the equations for a spherical object of uniform density and then finding the maximum mass and pressure that can be sustained against gravitational collapse at a given radius. This results in the 4/9 limit.
Buchdahl's theorem has important implications in astrophysics, as it sets a limit on the maximum size and mass that a neutron star or other compact object can have without collapsing into a black hole. It also helps to understand the structure and behavior of stars and other astronomical objects.
No, Buchdahl's theorem has not been proven experimentally. It is a mathematical proof based on general relativity and has not been directly tested in a laboratory setting. However, observations of astronomical objects, such as neutron stars, have supported the predictions of Buchdahl's theorem.