Schwarzschild metric

In Einstein's theory of general relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the gravitational field outside a spherical, non-rotating mass such as a (non-rotating) star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or Sun. According to Birkhoff's theorem, the Schwarzchild solution is the most general static, spherically symmetric, vacuum solution of Einstein's field equations. A Schwarzschild black hole or static black hole is a black hole that has no charge or angular momentum. A Schwarzschild black hole has a Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass.

Related Topics:
Einstein's - General relativity - Gravitational field - Star - Planet - Black hole - Earth - Sun - Birkhoff's theorem - Static - Spherically symmetric - Vacuum solution - Einstein's field equations - Charge - Angular momentum

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The Schwarzschild solution is named in honour of its discoverer Karl Schwarzschild who found the solution in 1916, only a few months after the publication of Einstein's theory of general relativity. It was the first exact solution of Einstein's field equations (besides the trivial flat space solution). Schwarzschild had little time to think about his solution. He died shortly after his paper was published, as a result of a disease he contracted while serving in the German army during World War I.

Related Topics:
Karl Schwarzschild - 1916 - Flat space solution - World War I

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Schwarzschild's solution showed how the predictions of general relativity would deviate from the predictions obtained from Newtonian gravity. Using his solution for the gravitational field of the Earth and the Sun, the outcome of three classical tests of general relativity has been predicted. For about half a century they were the only experimental verification of general relativity. The classical tests are the gravitational redshift, the gravitational deflection of light and the perihelion shift of the planet Mercury. The perihelion shift of Mercury was one of the major problems that astronomers were trying to understand; when Einstein used Schwarzschild's solution to calculate the observed shift, he found that it was exactly (within experimental errors) the observed shift. For Einstein, this was the first major triumph of general relativity.

Related Topics:
Newtonian gravity - Classical tests of general relativity - Gravitational redshift - Gravitational deflection of light - Perihelion - Mercury

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The Schwarzschild black hole is characterized by a surrounding area, called the event horizon which is situated at the Schwarzschild radius, often called the radius of a black hole. Any non-rotating and non-charged mass that is smaller than the 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 nature is kind enough to form one.

Related Topics:
Event horizon - Schwarzschild radius - Einstein field equations - General relativity

~ ~ ~ ~ ~ ~ ~ ~ ~ ~