Black hole is a region in space-time, whose gravitational pull is so great that it could not even be left by the objects moving at the speed of light, including quant of light. The border of this region is called the event horizon, and its typical size is the gravitational radius. In the simplest case of spherically symmetric black hole, it is equal to Schwarzschild radius.
In theory, the possibility of the existence of such space-time regions is based on some exact solutions of Einstein’s equations, the first of which was received by Charles Schwarzschild in 1915. The inventor of the term is unknown, but the designation itself was promoted by John Archibald Wheeler and first publicly used in popular lectures Our Universe: the Known and Unknown, December 29, 1967. Earlier such astrophysical objects were called “stars” or “collapsed stars” as well as “frozen stars.”
The question of the real existence of black holes is closely related to how true the theory of gravitation, which shows their existence, is. In modern physics, gravitation theory, confirmed experimentally, is the general relativity theory (GRT), confidently predicting the formation of black holes (but their existence possible and within the other (not all) models, see: alternative theories of gravitation). Therefore, the observed data are analyzed and interpreted in the context of GRT, although, strictly speaking, this theory is not experimentally confirmed for the conditions corresponding to the region of space-time near black holes of stellar masses (but is well confirmed in the terms of supermassive black holes).
Therefore, allegations of direct evidence of the black holes existence, strictly speaking, should be understood in the context of the confirmation of the existence of astronomical objects, of such density and mass, as well as with some other observable properties, which allow you interpret them as black holes by GRT.
In addition, black holes are often referred to as objects, not strictly related to the above definition, and only the approaching in their properties to a black hole — for example, it can be collapsing stars in the later stages of collapse. Contemporary astrophysics do not give much attention to this fact, since the observed manifestations of “almost collapsed” (“frozen”) and “the present” (“eternal”) black hole are virtually the same. This is because the differences of physical fields around a collapsed star from those of the “eternal” black hole is reduced by exponential laws with the characteristic time of the gravitational radius, divided at the speed of light.
There are 4 scenarios of the black holes formation, two realistic ones: gravitational collapse (contraction) of sufficiently massive stars; the collapse of the central part of the Galaxy, or primeval galaxy gas; and two hypothetical: the formation of black holes immediately after the Big Bang (primordial black holes); in the high-energy nuclear reactions.
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