What is Schwarzschild metric: Definition and 106 Discussions
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916, and around the same time independently by Johannes Droste, who published his much more complete and modern-looking discussion only four months after Schwarzschild.
According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum. A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass.
The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon, which is situated at the Schwarzschild radius, often called the radius of a black hole. The boundary is not a physical surface, and a person who fell through the event horizon (before being torn apart by tidal forces), would not notice any physical surface at that position; it is a mathematical surface which is significant in determining the black hole's properties. Any non-rotating and non-charged mass that is smaller than its Schwarzschild radius forms a black hole. The solution of the Einstein field equations is valid for any mass M, so in principle (according to general relativity theory) a Schwarzschild black hole of any mass could exist if conditions became sufficiently favorable to allow for its formation.
Hello, I've enjoyed reading these forums for a while now as they have lots of great insight! Today I decided to register so I can ask a question that's been bothering me for a few days now. (By the way, I'm moving onto my senior year as a physics major)
So yea, to the question. I have been...
Light rays in the schwarzschild metric satisfy the differential equation
\frac {d^2u} {d\phi^2}+u=3Mu^2
u=1/r
I want to show that there is closed orbits with constant radius and also calculate the radius of the orbits as a function of the Schwarzschild radius.
Can anyone help...
Well, I think I finally figured out how to get good values for the local values of the Christoffel symbols (aka local gravitational accelerations) in the Schwarzschild metric. Some of the results are moderately interesting, though there is one point that still makes me wonder a bit.
If we...
What evidence is there that the schwarzschild metric is valid inside a black hole (as opposed to outside the Sun where evidence comes in the form of mercury's perihelion)?
Also, if a black hole is made from photons, would it be massless and move at
the speed of light?
The Schwarzschild Metric is only valid for R>2M, What are the units used here? Obviously R and M should have incompatible units...so how can any comparison of this type be made?
i'm toying around with the schwarzschild metric using it to find distances from a star in sphereical coordinates.
the metric is:
g** =
1/(1-2M/r) 0 0 0
0 r^2 0 0
0 0 r^2sin(theta)^2 0
0 0 0 -(1-2M/r)...