# 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.

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1. ### I Eddington-Finkelstein coordinates for Schwarzschild metric

I'm studying Eddington-Finkelstein coordinates for Schwarzschild metric. Adopting the coordinate set ##(t,r,\theta,\phi)##, the line element assumes the form: $$ds^2 = \left(1 - \frac{R_S}{r}\right)dt^2 - \left(1 - \frac{R_S}{r}\right)^{-1}dr^2 - r^2 [d\theta^2 + (\sin{\theta})^2d\phi^2],$$...
2. ### I Schwarzschild Metric & Particle Absorption

The Schwarzschild metric implies a potential different from that of Newtonian gravity. Is there a relationship between it and the process by which particles can be absorbed by other particles? (I haven't studied QFT yet)
3. ### I Equations of motion for the Schwarzschild metric (nonlinear PDE)

I'm working through some things with general relativity, and am trying to solve for my equations of motion from the Schwarzschild Metric. I'm new to nonlinear pde, so am not really sure what things to try. I have 2 out of my 3 equations, for t and r (theta taken to be constant). At first glance...
4. ### I How to Measure Speed of Light & Is It Constant?

The question constantly arises how the speed of light is measured and what does it mean that the speed is constant, including at remote points for the observer, including at points beyond the local frame of reference, as you understand it in general relativity (GR). First of all, it should be...
5. ### I Adapting Schwarzschild Metric for Nonzero Λ

So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...

48. ### B Schwarzschild Metric Derivation?

Hi, I was wondering if anybody could help me understand the derivation of the Schwarzschild metric developed by the author of mathpages website. Rather than reproduce all the equations via latex, I have attached a 2-page pdf summary that also points to the mathpages article and explains my...
49. ### B Schwarzschild Metric: Non-Rotating Black Holes & Examples

Hello I have been reading about Schwarzschild metric and scources what I read said that Schwarzschild metric is used to describe a non-rotating black holes. And what I can not understand is what can you calculate with it? It would be good if you give some examples where you can use it.
50. ### A Einstein & Light Deviation: Compute w/o Schwarzschild Metric

How did Einstein compute the amount of light deviation due to the Earth's gravitational field when the Schwarzschild metric was not known yet?