The Schwarzschild Solution
The embedded or worldline diagram makes visualizing the curvature of Schwarzschild geometry easier. Think of normal space and time as a flat surface. With any object, this flat surface curves downward because mass curves space, which creates gravity. As you can see with a singularity, our diagram of space and time stop at the point.
The Schwarzschild Radius (rs) or Event Horizon is the distance from the point mass at which the gravitational field is so powerful that the black holeís escape velocity is greater than the speed of light.
rs = 2 G M / c2
G = Gravitational Constant; M = Mass; c = speed of light;
The photon sphere is the distance from the singularity that light can have orbit around the black hole. The photon sphere is 1.5 Schwarzschild Radii from the singularity. Past the photon sphere, nothing can maintain a circular orbit around the black hole.
Mass is the only property a Schwarzschild black hole has. A Schwarzschild black hole is the basic description of a still-standing black hole, however stars in nature rotate. You can't apply Schwarzschild to real stars because when a spherical object spins it drags spacetime along with it. To describe a rotating black hole, we need another solution.
Continue to The Kerr Solution.
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