I already wrote this somewhere else. If the curvature of space around a gravity source is proportional to the square root of distance, like the gravitational time dilation formula, then negative distance (internal space) becomes a complex number and gets an extra dimension - the real number and the imaginary. Is there any truth to that?

Gravity doesn't work like that. If it did, weird things would happen just by going underground.

Negative distance makes absolutely no sense, and even if it did, center of mass is a point which by definition has no volume meaning you can't be inside it.

Given negative radius (internal radius), we might get an internal space coordinate

a negative radius isn't physically possible. the closest two bodies can be is coincident, which is the case where r=0.

a back hole is just a pile of really dense matter. so dense that the escape velocity of the gravitational field it creates exceeds the speed of light. while its very dense, its not infinitely dense, and has volume and radius as well as mass (LOTS of mass). and the radius is non-negative.

a back hole is just a pile of really dense matter. so dense that the escape velocity of the gravitational field it creates exceeds the speed of light. while its very dense, its not infinitely dense, and has volume and radius as well as mass (LOTS of mass). and the radius is non-negative.

Eh. A "black hole" is typically describing the event horizon. It's not a solid ball, it's just the distance at which all light cones point inwards. From the perspective of a local observer entering the event horizon, nothing actually happens when you cross it. Going strictly by general relativity, no force is strong enough to resist the force of gravity inside the event horizon and so the entirety of the mass is squashed into an infinitesimal point* called a singularity. The singularity does have infinite density, if you're taking a relativistic view. For a variety of reasons, this is a pretty shoddy model and quite a lot of work has gone into coming up with something that is consistent with the rest of our body of physics knowledge. While there are many proposals, I don't think there are any good answers.

* The singularity is a point in the case of a non-rotating black hole. Keeping things simple.

a back hole is just a pile of really dense matter. so dense that the escape velocity of the gravitational field it creates exceeds the speed of light. while its very dense, its not infinitely dense, and has volume and radius as well as mass (LOTS of mass). and the radius is non-negative.

Eh. A "black hole" is typically describing the event horizon. It's not a solid ball, it's just the distance at which all light cones point inwards. From the perspective of a local observer entering the event horizon, nothing actually happens when you cross it. Going strictly by general relativity, no force is strong enough to resist the force of gravity inside the event horizon and so the entirety of the mass is squashed into an infinitesimal point* called a singularity. The singularity does have infinite density, if you're taking a relativistic view. For a variety of reasons, this is a pretty shoddy model and quite a lot of work has gone into coming up with something that is consistent with the rest of our body of physics knowledge. While there are many proposals, I don't think there are any good answers.

* The singularity is a point in the case of a non-rotating black hole. Keeping things simple.

What actualy made scientific conclusion that inside a black hole is a singularity? Since the strength of gravity force is not influenced by density, just by the mass, the density causes the object to be just small enough to accelerate attracted objects enough fast before collapsing right? Consider earth to be as big as a tenis ball, but still having mass of earth. Would objects falling towards it cross speed of light at same particular distance ? Would the ball be singularity? Would the ball still be able to keep that much mass in such dense state just by having gravity of that mass? Even we humans on earth, can cause matter to turn into energy, so is black hole just keeping matter a matter, I think there is really something paranormal going on, since black hole dominates over condition that should just chain react anything, even unradioactive matter. We have never observed a black hole explosion, nor we do know nothing about black hole life time.

I think there is really something paranormal going on

Ah, the "black holes are dead ancestors" theory.

As for not seeing them, they've been witnessed quite a few times. There are two types of supernova event: the explosion of a re-igniting degenerate star, and the gravitational collapse of a star. The second one results in a black hole if there was enough mass to form one.

I already wrote this somewhere else. If the curvature of space around a gravity source is proportional to the square root of distance, like the gravitational time dilation formula, then negative distance (internal space) becomes a complex number and gets an extra dimension - the real number and the imaginary. Is there any truth to that?

No. There's no such thing as "internal space" in the sense that you mean. Remember, a stellar object is composed of many smaller pieces that are all exerting their own gravitational acceleration. When you descend into the "interior" of the Earth, their gravity pulls on you no less than they did before. The end result is that as you get deeper, the matter above you pulls you back up, so the aggregate acceleration due to gravity actually decreases. If you were somehow able to get to the Earth's center of mass, you would feel weightless because the Earth's mass would be pulling you in every direction at once. In fact, if the Earth were hollow, if you managed to get into the hollow space you would be weightless inside. Of course, this is neglecting tidal forces from the other bodies in the solar system and the huge internal pressure of the Earth's core.

That you're talking about black holes without knowing about the shell theorem makes me worry that you haven't done sufficient research.

What actualy made scientific conclusion that inside a black hole is a singularity?

My understanding is that nothing has actually made that scientific conclusion.

To be more specific, singularities arise as a consequence of the equations of relativity, but all that means is that relativity predicts singularities. It doesn't mean anything else. On the other hand, quantum mechanics (again, my understanding) says that singularities can't exist, and therefore the only scientific conclusion here is that our theories of the universe are not yet complete.

The singularity does have infinite density, if you're taking a relativistic view.

which implies a zero radius, as its mass can't be infinite, as it hasn't swallowed all mass in the universe.

and of course this is theoretical, no one has been beyond an event horizon to determine if a singularity has zero radius and infinite density or not. its a scientific "best guess".

but its probably safe to say a singularity is of extremely small radius and extremely high density at the very least - even if we can't tell for sure.

but more to the point of the OP, its also probably pretty safe to say that the radius of a singularity is non-negative.

frankly, a zero radius doesn't even compute (to me). after a certain point, you can't smoosh the protons, neutrons , and electrons any closer together. unless some neato thing happens in extreme gravity that lets sub-atomic particles co-exist in the same physical space at the same time. hey you never can tell, sometimes you get some odd things happening at the extremes of things like gravity or heat or cold.

the density causes the object to be just small enough to accelerate attracted objects enough fast before collapsing right?

the density is a function of its volume and mass. its volume is a function of its compressability, and the forces acting upon it. in the case of a black hole, its own gravity is the only significant force. so as a black hole captures more material, its mass and gravity increase, but the compressability of the captured material is on the average the same (IE space debris), so with increased gravity, its gets compressed more, thus increasing the density. theoretically this would continue until the weak nuclear forces prevented the sub-atomic particles from coming any closer together.

density is not the thing that "sucks stuff" past the event horizon, never to return, its gravity. as soon as a body accumulates enough mass such that the escape velocity of its gravitic field exceeds c=speed of light, it becomes a "black hole" - so called because not even light can escape its field of gravity.

think the space shuttle and earth escape velocity. same idea, much bigger scale. and we all generate gravitic fields, even you and me and the paperclip on the desk. but they're so weak compared to the earth's that you can't even tell they're there.