The Schwarzschild Solution
In 1916, Karl Schwarzschild, a German Physicist,
formulated a solution to Einstein’s field equations that describes how
spacetime curves around a spherical, static object known as Schwarzschild
Geometry. This solution is now used to describe simple black holes.
A Simple Black Hole
A Schwarzschild black hole is a
perfectly spherical, static and non-rotating black hole. Basically, it
is a point mass (with no height, width or depth) of infinite density or
a singularity in the center with a gravitational field surrounding
it. At the singularity, space and time as we know it stop.
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.
Schwarzschild Radius
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 hole’s escape velocity
is greater than the speed of light.
rs = 2 G M / c2
G = Gravitational Constant; M = Mass; c = speed of light;
Photon Sphere
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.
Properties
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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