BLACK HOLE "not punctual" or Non-Singular Black Hole (© Angel Torregrosa Lillo) (updated 2025)
[version española]

Summary

This article proposes and explores the possibility of non-singular black holes, based on the time dilation effect caused by gravity, which intensifies as one approaches the event horizon, potentially preventing the formation of a point-like singularity.

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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.

In our discussion of black hole formation, we noted that a star could theoretically collapse into a single point, resulting in a singularity characterized by infinite density and space-time curvature, as well as imaginary time within its interior. However, from the perspective of a distant observer, a body falling toward a black hole would take an infinite amount of time to reach the event horizon. This is due to the contraction of lengths and the slowing of time as one approaches the event horizon (see the section on length contraction in a gravitational field for a demonstration). Consequently, the velocity of the falling object, as observed externally, approaches zero, suggesting that a black hole may never fully form.

But in addition to this, it occurs to me 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 it stops as we approach the event horizon.

Moreover, we propose that an intrinsic mechanism—namely, the extreme time dilation near the event horizon—could halt the final collapse into a singular point. This hypothesis suggests that, even if matter surpasses the event horizon, the singularity problem may be avoided because time effectively stops at the event horizon.

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 scenario, time would be frozen throughout the star’s volume (the event horizon would be a three-dimensional sphere, not merely a spherical surface). Consequently, the collapse would halt, even if the pressure sustainable by neutrons is exceeded and neutron fusion occurs. For a star undergoing neutron collapse, achieving this density distribution would stop the collapse by freezing time.

To achieve this distribution, we assume that the gravitational field inside a star is equivalent to that produced by the mass below a given point, as the gravitational field within a spherical shell is zero. 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.

At greater depths, then, the density increases inversely proportional 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.

This type of black hole may be common, as neutron fusion during a stellar implosion begins at the star’s core. The time-freezing condition would first occur at the center, preventing further matter fusion there. This effect would propagate outward, layer by layer, creating the calculated density distribution and forming a solid black hole from the event horizon inward, without a singularity. This concept echoes the "frozen star" model proposed by Oppenheimer and Snyder in 1939 and revisited by Shuang-Nan Zhang in 2010.

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.

This hypothesis aligns with alternative models, such as the "gravastar" proposed by Mazur and Mottola (2001), which describes a Bose-Einstein condensate with negative pressure (( p = -\rho )) inside the object, eliminating the event horizon. Other models suggest black hole interiors may consist of dark matter, dark energy, or exotic matter, often termed "black hole impostors."

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

Bibliography

 

[black holes index]

 

INTRODUCTION / HOW THE BLACK HOLES ARE FORMED / SPECIAL RELATIVITY AND BLACK HOLES / GENERAL RELATIVITY AND BLACK HOLES / BLACK HOLES DETECTION / The NON- PUNCTUAL BLACK HOLE / SPACE-TIME graphics on STAR COLLAPSE / HOLES In ETERNAL FORMACION, ETERNAL BLACK HOLES And OTHER MATHEMATICAL CONCEPTS