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Is a Black Hole Singularity logical?

From wikipedia:

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A singularity is a location in spacetime where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system. The quantities used to measure gravitational field strength are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. Since such quantities become infinite within the singularity, the laws of normal spacetime cannot exist.

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Solutions to the equations of general relativity or another theory of gravity (such as supergravity) often result in encountering points where the metric blows up to infinity. However, many of these points are completely regular, and the infinities are merely a result of using an inappropriate coordinate system at this point. In order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. scalars) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.
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When I looked for a reference with a description of a singularity I did not expect the utter nonsense above with several references to coordinate systems, perhaps even a point in a coordinate system. A coordinate system allows an observer to define a frame of reference. It is literally impossible for a physical behavior to depend on a coordinate system serving as a reference for the observer. That is like saying the earth's gravitational field changes depending on my specific latitude or longitude value or on the specific time on my watch, or gravity changes when I alternate between cartesian [and its XOY0Z0 zero reference] and GPS coordinate systems, one linear the other spherical. To offer such an explanation for a zero radius is ridiculous.

The basic description for a singularity is a mass at a single point so it has zero radius and infinite density. The force of gravity is so strong from this point source that light cannot escape, leading to the term black hole.

Fusion can compress nuclei to form heavier elements.That process requires substantial force to overcome the repulsion between the positively charged nuclei, but the protons remain intact. There is no imaginable force that can compress a proton to zero radius while it maintains its mass. There is no mass that can exist in a point, or a sphere with zero radius. It is not logical to propose something impossible.

Given a singularity does not have a logical explanation why is one proposed to exist in the universe?

The reason lies in the assumption: 'laws of normal spacetime cannot exist.' In practice a black hole and its singularity are placed where no other explanation is readily available.

Having a point source of gravity can be useful, though impossible. An accretion disk can be proposed to form around it.

For example the universe has many known X-ray sources but in many cases it has no counterpart in visible light. It is well known X-rays can be part of the spectrum emitted by synchrotron radiation generated by the interaction between an electric current and a magnetic field. These electromagnetic effects and their sources might not be visible but they could be measurable (such as the polarization of light). For example plasma can be in dark mode or glow mode depending on its excitation. Black holes are never accompanied by electromagnetic effects in their descriptions.

Cosmologists propose an alternate explanation for X-rays with this invisible source.
The black hole becomes responsible for the X-ray emission because as a point it could create an accretion disk around the invisible singularity and this disk could generate X-rays due to the high temperature in the disk.

All or nearly all X-ray sources in the universe having no visible counterpart will be assigned a black hole.

Currently there is no confirmed black hole in the universe.

The one proposed detection technique is: find a visible star in a valid elliptical orbit around the black hole. This has never been done. An attempt was done for the claimed black hole at the center of the Milky Way but a star with a valid orbit could not be found.

In case wikipedia is not an acceptable reference britannica also gets to the same point: zero volume. That is the common interpretation.

from britannica:
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At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite. For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity lying in the plane of rotation. In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. The singular region can thus be thought of as having infinite density.
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My conclusion:

A point source of gravity is not possible.
It is not logical to propose this theoretical concept as the solution for any actual observations.

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