Schwarzschild radius

Assembled from 18 blocks · 2 evidence · 15 related

1. Story
2. The radius at which the escape velocity of a spherical non-rotating mass reaches the speed of light, r_s = 2GM/c-squared. It is linear in mass, which is the single most useful thing to know about black holes and the least intuitive: doubling the mass doubles the radius, so density falls as the square of mass and a sufficiently large black hole is not dense at all. For the Sun the value is about 2.95 km; for the Earth about 8.9 mm; for Sagittarius A* at roughly four million solar masses it is about thirteen million kilometres, a tenth of the Earth-Sun distance; for M87* at about six and a half billion solar masses it is roughly nineteen billion kilometres, wider than the orbit of Pluto. The radius is a property of the geometry, not of any material surface, and Karl Schwarzschild who derived it in 1916 did not read it as a boundary of no return - that interpretation took another four decades. Not a place on Earth.
3. Knowledge
4. Schwarzschild radius
5. Karl Schwarzschild
6. Connections
7. Karl Schwarzschild
8. The event horizon
9. The photon sphere and the shadow
10. Time dilation near a horizon
11. Tidal stretching near a black hole
12. Einstein presents the field equations of general relativity
13. Schwarzschild solves the field equations for a point mass
14. Schwarzschild radius
15. Schwarzschild solves the field equations for a point mass
16. Evidence
17. The first exact solution of the Einstein field equations for the vacuum outside a spherical mass, containing the radius now named for its author. V55 VERIFICATION BASIS: the paper was NOT consulted in this session - WebFetch was refused by the network egress proxy for every host attempted and the WebSearch budget was exhausted before authoring began. Title, venue and page range are given from the author's recall of a canonical citation and must be checked.
18. Reports the first image of a black hole shadow, an asymmetric ring about 42 microarcseconds across, together with the array, observing campaign and imaging methodology. V55 VERIFICATION BASIS: not consulted in session; WebFetch to iopscience.iop.org and eventhorizontelescope.org was refused by the egress proxy and no search could be issued. Volume and article number are from recall of a canonical citation.