It is true that mathematics does present BH as a singularity and construed to be zero-point-mass (ZPM). Singularities are mathematical anomalies, similar to the math, in the middle-ages, that proved the motion of the planets, as observed from Earth, were epicycles. Even though the math was consistent, the explanation was wrong. In general, math can be used to just about verify anything. ZPM contradicts the idea that multiple things cannot occupy the same space at the same time.
Gravity is a consequence of the BH, as the force of the gigantic mass displacing an elastic medium and it trying to restore itself to equilibrium toward the center-of-mass (CM) of the BH. Thinking of space as an elastic medium (a filled vacuum) is nomore radical than space-time. The only difference is the medium does not invoke time as a dimension. The medium is a three-dimensional volume. The stress and strain around a displacing mass is consistent with Newton. Contour around mass embedded in space, also, is similar to gravity in space-time.
There are two ways a BH is detectable. 1) Infra-red (IR) or 2) Light emitted at the event-horizon (EH). The EH is light emitted from the electrons being stripped, by heat from the star, as its atoms plummets into the BH; otherwise it is black, because it has no electrons. In other words, the light from the EH are the remnants of the destroyed atoms.

The answer to your question "are black holes gigantic neutron stars" is: no.

As for the rest of your post - I don't detect any physics questions. However - your assertion that epicycles as envisioned by people in the middle ages somehow involved singularities is wrong. They were merely trying to come up with a geometric explanation for the observed motion of the planets, based on a flawed assumption that orbital geometry must be based on circles, or circles within circles. But no matter how many layers of circles within circles within circles they tried the math could never quite match the observed data. It was Keppler who made the leap to think about ellipses instead.

The answer to yuor question "are black holes gigantic neutron stars" is: no.

As for the rest of your post - I don't detect any physics questions. However - your assertion that epicycles as envisioned by people in the middle ages somehow involved singularities is wrong. They were merely trying to come up with a geometric explanation for the observed motion of the planets, based on a flawed assumption that orbital geometry must be based on circles, or circles within circles. But no matter how many layers of circles within circles within circles they tried the math could never quite match the observed data. It was Keppler who made the leap to think about ellipses instead.

I was not attributing singularities to the middle-ages or are you deliberately misconstruing my post?

are you deliberately misconstruing my post?

You wrote: "Singularities are mathematical anomalies, similar to the math, in the middle-ages, that proved the motion of the planets, as observed from Earth, were epicycles." Ok - so perhaps you didn't explicitly say that the epicycles math was based on singularities, so I will amend my response to say that the math was not based on anomalies.