Gravitational Radius


Also found in: Dictionary.

gravitational radius

[‚grav·ə′tā·shən·əl ′rād·ē·əs]
(relativity)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

I. D. NOVIKOV

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
As we conclude on the basis of our book Inside Stars [2], the ratio of the gravitational radius and the space breaking radius to the physical radius a (i.e.
This will be on the order of the system's Compton wavelength, [[lambda].sub.m] [equivalent to] [l.sub.p][M.sub.Pl]/m, providing the additional constraint on the gravitational radius
is a combination of requiring the particle to rest within a sphere of radius r = [r.sub.H] and the probability that [r.sub.H] is the gravitational radius. These are, respectively, calculated as
Rewriting (15) using the substitution [DELTA]x [right arrow] R and [DELTA]p [right arrow] M, one can define both a generalized Compton radius (approaching from the sub-Planckian regime) and a gravitational radius (approaching from the super-Planckian regime) [4]:
an external observer sees the star asymptotically shrinking to its gravitational radius. This result contradicts directly Penrose's description of the OS results and was verified by me in [1].
It should be noted that in the exterior, and hence in what should now be recognized as the universal, time frame the collapsar's shrinkage to the gravitational radius takes an infinite lapse of time.
This is the real significance of the event horizon, but it is my contention that a real collapsar, with an internal pressure resulting from the intervention of forces other than gravitational, stops shrinking before it reaches the gravitational radius. For example, we have investigated [7] a collapsar whose equation of state is an idealized form of neutron [fluid.sup.*], and for which, above a certain mass, its maximum density lies between the event horizon and the photonsphere.
This apparent little problem is overcome by using [??] instead of h in the dimensional analysis approach and by putting the Compton wavelength equal to [pi] multiplied by the Schwarzschild or gravitational radius in the approach.
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.
What physical basis is there in asserting the equivalence of the Compton wavelength and the Schwarzschild or gravitational radius of a particle?