Construct · 1 fields · 3 citations

Schwarzschild radius: a standalone construct

One name. One construct. A landmark on the map.

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Schwarzschildradius1 CONSTRUCTSchwarzschild radiusSCHWARZSCHILD · HORIZON

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General relativity

The radius of the event horizon of a nonrotating black hole, r = 2GM/c^2

Karl Schwarzschild's 1916 paper gave the first exact solution of Einstein's field equations of general relativity, describing the gravitational field around a nonrotating, uncharged spherical mass, and it introduced the characteristic length now named for him: r = 2GM/c^2, where G is the gravitational constant, M the mass, and c the speed of light. At that radius the escape speed formally equals the speed of light, and if a mass is compressed within it the surface becomes an event horizon, the one-way boundary from inside which no light or matter can reach the outside. J. Robert Oppenheimer and Hartland Snyder's 1939 study of continued gravitational contraction described how a collapsing star can shrink inside this radius, and David Finkelstein's 1958 analysis showed that the radius is not a true singularity but exactly such a horizon. The Schwarzschild radius scales in direct proportion to mass, so it is roughly 3 kilometres for the mass of the Sun and about 9 millimetres for the mass of the Earth, and it fixes the size of the event horizon of any nonrotating black hole. It is distinctive as the length scale at which gravity becomes strong enough to trap light, marking the outer boundary of a black hole and the point where the spacetime around a compact mass departs sharply from Newtonian gravity.[1][2][3]

Unit
A length: r = 2GM/c^2, the radius (in metres) of the event horizon corresponding to a given mass
Recovery means
Not applicable
Measured by
Computed directly from a body's mass as r = 2GM/c^2; the corresponding horizon size is inferred observationally from black-hole mass estimates and from event-horizon imaging

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Nearby constructs

singularity3 fields · 5 citationsjingle · one word, three constructsmass3 fields · 9 citationsjingle · one word, three constructsmetric4 fields · 4 citationsjingle · one word, four constructs

References

  1. Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, 189–196.
  2. Oppenheimer, J. R., & Snyder, H. (1939). On continued gravitational contraction. Physical Review, 56(5), 455–459. https://doi.org/10.1103/PhysRev.56.455
  3. Finkelstein, D. (1958). Past-future asymmetry of the gravitational field of a point particle. Physical Review, 110(4), 965–967. https://doi.org/10.1103/PhysRev.110.965

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