Schwarzschild radius

or gravitational radius

Radius inside which the gravitational attraction between a body's particles must cause its irreversible gravitational collapse, named for Karl Schwarzschild. This is thought to be the final fate of the most massive stars (see black hole). The gravitational radius (R_g) of an object of mass M is given by R_g = 2GM/c², where G is the universal gravitational constant and c the speed of light. For a star like the Sun, the Schwarzschild radius would be about 1.8 mi (3 km).

gravitational radius [‚grav·ə′tā·shən·əl ′rād·ē·əs]

(relativity)

Gravitational Radius

in the general theory of relativity, the radius of a sphere on which the force of gravitation due to mass m that is entirely inside the sphere tends to infinity. The gravitational radius is determined by the mass m of a body and is given by the formula r_g = 2Gm/c², where G is the constant of gravitation and c is the velocity of light. The gravitational radius of ordinary astrophysical objects is usually insignificantly small compared with their actual dimensions; for the earth r_g ≈ 0.9 cm, and for the sun r_g ≈ 3 km.

If a body is compressed to the dimensions of its gravitational radius, no forces will be able to check its further compression under the action of gravitational forces. Such a process, called relativistic gravitational collapse, can occur with stars that are sufficiently massive (calculation shows that they must have a mass greater than twice the solar mass) at the end of their evolution: if, having exhausted its nuclear “fuel,” a star does not explode or lose mass, it must experience relativistic collapse, undergoing compression to the dimensions of its gravitational radius.

In case of gravitational collapse, neither radiation nor particles can escape from inside a sphere of radius r_g. From the point of view of an observer remote from a star whose dimensions approach r_o, the passage of time is infinitely slowed down. Therefore, for such an observer the radius of the collapsing star approaches the gravitational radius asymptotically but never becomes less than it.

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