Ray of Schwarzschild

The ray of Schwarzschild is defined like the critical ray envisaged by the Géométrie of Schwarzschild, in on this side which nothing can escape: if a star or any other object reaches a ray equal or lower than its ray of Schwarzschild (which depends on its mass, cf below), then it becomes a Black hole, and any object approaching at a distance this one lower than the ray Schwarzschild cannot escape from it. The term is used in Physique and Astronomie to give an order of magnitude of the characteristic size for which effects of General relativity become necessary for the description of objects of a given mass. Only objects which is not black holes and whose size is of the same order that their ray of Schwartzschild are the neutron stars (or Pulsar S), as well, curiously, as the observable Univers in its entirety.

The term owes its origin with the German Astrophysicien Karl Schwarzschild, discoverer in 1916 of the first exact solution to the equations of Einstein, which proved later on to describe a black hole (see metric of Schwarzschild). Incidentally, Schwarzschild means in German black shield , term particularly adapted to the concept of black hole.

The distortions of the Espace-temps in the vicinity of a black hole make the concept of distance a little subtle. The term of ray of Schwarzschild refers in fact with the ray which one would associate with an object of a Circonférence given in Euclidean Géométrie: it is not possible to measure the ray of a black hole while crossing it (since nothing can escape from it), it is on the other hand possible to measure the circumference of it by making the turn without penetrating there.

This ray is of this fact called horizon of the black hole (one cannot see what it occurs there inside). The ray of Schwarzschild is proportional to the mass of this one, and is determined by the following relation:

R_s = \ frac {2GM} {c^2} \ approx \ frac {M} {M_} \ times 2.950 \; {\ rm m \ serious {E} very},

where $G$ is the Constante of gravitation, M the mass of the black hole, M _o the mass of the Sun and $c$ the Speed of light. The exact value of this ray is modified if the object considered has a electric Charge nonnull or a kinetic Moment. In practice, only the kinetic moment plays a part, the electric charge being negligible in all the configuration where black holes are produced, but in all the cases, the ray of Schwarzschild expressed in kilometers is about three times the mass of the object considered expressed in solar masses.

Because of smallness of the $G quantity/c^2$ in the usual units, the ray of Schwarzschild of an astrophysical object is very small: for the mass of the Ground, it is from only 9 Millimètre S. Since the average radius of the Earth is approximately 6370 Kilomètre S, the Earth should be compressed until reaching 4×10²⁶ time its density current before being able to crumble in a black hole: it is not easy to train black holes of low mass. A stellar Black hole typical has a ray which amounts of tens of kilometers. For an object of the mass of the sun, the ray of Schwarzschild is of approximately 3 kilometers, which is quite lower than the 700 000 kilometers of the current ray of the Sun. The ray of Schwarzschild of the Sun is also appreciably smaller than the ray than the Sun will have after having exhausted its nuclear fuel, that is to say several de thousands; kilometers when it becomes a white Naine. More massive stars can however crumble as black holes at the end of their life. In the case of a supermassif Black hole, like those which one finds many in the center of Galaxie S, the black hole has a mass of a few million to several billion solar masses, for a ray of several million to several billion kilometers, that is to say less than the size of the orbit of Neptune. This small size makes difficult the direct detection of the black holes, for lack of a angular Résolution sufficient. There remains however possible to be able to directly color the central black hole of our Galaxy by methods of Interférométrie at very long base (VLBI). Possible paramount black holes, of very low mass (a few billion ton S) could possibly exist. Such black holes would be of microscopic size, and would be detectable only by their Rayonnement, resulting from the phenomenon of evaporation of the black holes.

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