Gravitational Radius

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gravitational radius

[‚grav·ə′tā·shən·əl ′rād·ē·əs]

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 rg = 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 rg ≈ 0.9 cm, and for the sun rg ≈ 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 rg. From the point of view of an observer remote from a star whose dimensions approach ro, 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.


References in periodicals archive ?
Another derivation involves the consideration of a body whose Compton wavelength equals its Schwarzschild or gravitational radius [1].
Hence, even if the equality of the Compton wavelength to the gravitational radius of curvature of a point-mass could be admitted, the alleged Planck particles would necessarily be point-masses, which are not only fictitious but also contradict the very meaning of the Compton wavelength and, indeed, the foundations of Quantum Mechanics.
dagger]) According to today's mainstream concepts, the gravitational radius [r.
From this it is argued that the Universe was born from an Inversion Explosion of the primordial particle (pre-particle) whose outer radius was that of the classical electron, and inner radius was that of the gravitational radius of the electron.