BLACK HOLE not punctual (© Angel Torregrosa
Lillo)
[version
española]
In the section about the formation of the black holes we spoke of which a star could be contracted until being a simple point. This as much represented a singularity of density as of space curvature (infinite density and curvature), in addition to imaginary times in its interior.
Nevertheless a body that falls towards a black hole would take an infinite time, from the point of view of an observer sufficiently moved away, since the lengths are contracted as we approached the event horizon (in the section contraction of lengths in a gravitational field we can see a demonstration of this contraction) and then, although the speed stays from the point of view of the observer that falls, this one will be diminishing towards zero for the external observer. Thus exist the possibility that never the black hole were formed.
But in addition to this, go to mi mind the possibility that something exists that can stop this final collapse towards a point (if that is possible) and this is the slowing of time until their detention as we approached to the event horizon.
Thus, it is possible to expose the hypothesis that, in the supposition that in spite of all, the matter could be collapsed and could surpass the event horizon, the singularity problems could be avoided because of the fact that in the event horizon the time stops .
Let us remember that according to general relativity the speed of the light diminishes (we can see a demonstration in the section restraining the light of the relativity section ) as it approaches a mass (fact verified sending and receiving radio signals to artificial satellites located near behind the Sun). Then, if the light brakes until stopping, we can also suppose that all falling and movement will stop when approaching to the event horizon)
Let us suppose a star whose distribution of inner densities is so that the situation that characterizes an event horizon ensue in all the volume of the star.
In this case the time would be stopped in all the volume of star (the even horizon would be a sphere, not a spherical surface) and therefore the collapse from this point would not happen even if the bearable pressure by neutrons were surpassed, and neutrons already were merging.
Thus in a star collapsing itself its neutrons, if this distribution of densities were obtained, the collapse would stop when stopping the time.
In order to obtain this distribution we must consider that the gravity inside a star is equal to that it would have if we remove a spherical wreath just above from the point in which we want to calculate the gravitational field strenght (because inside a spherical crown the gravitational field is annulled). Thus the calculations are the same as for a point in the surface but considering only the volume that remains below this point.
Then according to the equation (4) we have M'/r' has to be a constant relation in all the star being M' the sphere mass with radio = r' with center in the same center of the star. Thus we have
(12)
and therefore if we isolate the mass
M'=Kr' (13)
On the other hand, the total mass of the star will be equal to the sum of all the differentials of mass, being a mass differential equal to the density in a given sphere's point, s (x) multiplied by the differentialof volume, that will be equal to the area of the spherical surface multiplied by a radio differential. Therefore we will obtain that
(14)
An evident solution for s (x) so that the integral results Kr' is
(15)
being x the distance from the point of the star we studied to the center.
To greater depth we'll have greater inversely proportional density to the square of the radius. This takes us to an infinite density in the star center, but we must consider that when the radius becomes zero the mass also tends to zero, which makes this situation more acceptable.
It could be that this type of black hole was common in all the black holes, since in a stellar implosion the neutron fusion would begin to be made in the center of the star, and the situation of halting time would begin to occur in the center of the star preventing the fusion of more matter in this point. This situation would be extended layer to layer outwards being created a distribution of densities like that I have calculated, and therefore a solid black hole from the even horizon towards the interior. Without singularity.
Anyway, as several readers have commented me, all that would be from the point of view of an external observer (the most far away possible), that is the same that from a point of view of a cosmic time (I speak of it in the section on the cosmic microwaves background ), whereas a local observer that fell towards the black hole will not notice this halting of time because for each one his time is the natural one. Therefore, if that person watched towards the neighboring star would see it aging and turning faster than normal turning, because for him the time of the neighboring star would be accelerated. As we see, the perception of the time is relative.
In the next page we can see how may be the space-time graphics of a star colapsing as the clasical model and as this hypothesis
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