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For example, the radius of the Sun is approximately 700 000 km, while its Schwarzschild radius is only 3 km. The singularity at r = r s divides the Schwarzschild coordinates in two disconnected patches. The exterior Schwarzschild solution with r > r s is the one that is related to
The Schwarzschild radius or the gravitational radius is a physical parameter in the ... is a coordinate singularity, ... (in this example, 997 kg/m 3, the ...
Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere the coordinate system is used. An example of such a conical singularity is a cosmic string and a Schwarzschild black hole. [15]
This is unfounded because that law has relativistic corrections. For example, the meaning of "r" is physical distance in that classical law, and merely a coordinate in General Relativity.] The Schwarzschild metric can also be derived using the known physics for a circular orbit and a temporarily stationary point mass. [1]
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. [1] Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius.
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres.In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres.
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.
Schwarzschild solution in Schwarzschild coordinates, with two space dimensions suppressed, leaving just the time t and the distance from the center r. In red the incoming null geodesics. In blue outcoming null geodesics. In green the null light cones on which borders light moves, while massive objects move inside the cones.