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?

A few concerns.

The biggest is that you are using the simplification as the basis for your theory.

There are many ways to think about what happens around the borders of a black hole. While it is popular to think of it as a curvature of space/time, that is a simplification that makes it easier to explain to a lay-person. You've got a big heavy elastic surface, you put something big and heavy on it and a dent or bend is visible, the concept is communicated.

While the concept works readily enough for an ELI5-style world, it gets into some complicated PhD-style mathematics and theories. There is the equivalence principle that comes into play between gravity and mass, the relative dilation of both time and space, and a bunch of other stuff that it interesting but ultimately makes my eyes glaze over when Peter (my blackhole-studying brother) starts discussing it all. The curvature of space isn't really a curvature of all -- not in the spatial sense -- but a compression/dilation based on the interplay between gravity and mass at extreme values.

The stretchy surface of space/time simplification is not physically accurate, it is just an easy way to explain it.

As for complex or imaginary numbers adding a spatial dimension, note that numeric dimensionality does not equate to spatial dimensionality. You can add all kinds of non-spatial dimensions to the world around you. I've seen people try to add many other items as dimensions, such as colors and time. While they may serve as orthogonal dimensions for a specific purpose (e.g. the color of a thing is independent of the location of the thing) they are not additional spatial dimensions (Up/down, left/right, forward/back, and new dimension). All attempts to throw in a fourth spatial dimension break nearly all observable conditions and constants. Among the most easy of these would be the tunneling and slowing of motion; light moving along a fourth spatial dimension would appear to change speed in the three we can measure, but the magnitude of the speed of light measured in three dimensions is an apparent constant. Light moving completely along that fourth dimension would appear to be suspended in location, stopped or nearly stopped in the three dimensions we see resulting in a variable 3D speed of light, yet for all observations light moves at a constant speed in 3D.

A fourth spatial dimension would break most of the fundamental physical constants, like the speed of light, Planck's constant and the quanta of distances, magnetic and electric constants, and the rest. Is it possible that inside a black hole, somewhere we cannot currently directly observe, there are such radically different fundamental physics? Sure, why not. But it is an extremely long leap to make that inside a region of high mass like a black hole there would be a change to the fundamentals of physics.

If you want to imagine up a situation where inside a black hole you have a fourth spatial dimension, either (more likely) you will be on track for a creative science fiction novel, or (far less likely) you will be on the track for a PhD thesis in theoretical physics. If you have the mathematical chops to revise all the fundamental physics rules so they basically work with a fourth spatial dimension, then go for it. But I doubt that is the case.

Claims like "we are in a black hole that exists within another universe" are the kind of thing that always make me laugh at physicists, and makes me wonder why universities indeed put a lot of funds into such research (which I'm inclined to call "research").

Because a vast portion of said research checks out, and sometimes not just mathematically. Remember quantum fricking theory fact? With cutting edge topics there often appear to be no definitive answers for an extended period of time, because it's a notably complex question. In fact, that's why it's called theoretical physics. Without funding for your so-called "research", it would forever remain so and we would forever amount to little more than a fluke.

This is the kind of claim that's just funny to read - brushing off some of the smartest minds on the planet as lunatics and assuming their MO is to muck in the ultimate science fiction story just for kicks.

Do blackholes have an internal space?

Since you obviously didn't bother to google this, let me help you out there ;)

Your point of view as a human is the point of view of a microbe living on a mite's butt living on a camel's butt. The camel looks at the sun setting on the horizon and thinks "this is where the world ends". But you look at the mite's butt and think "this is where the world ends". There is no way you could possibly ever see the horizon, or the "end" of the world.

So we shouldn't even try? We shouldn't even waste time on conjecture?

Just because something doesn't have an immediate practical effect doesn't mean it's worthless.

Given the vast amounts of other crap we waste money on (weapon systems, garbage tv, anything that Michael Bay does), I have no problem whatsoever funding this kind of research.

Because a vast portion of said research checks out, and sometimes not just mathematically. Remember quantum fricking theory fact? With cutting edge topics there often are appear to be no definitive answers for an extended period of time, because it's a notably complex question. In fact, that's why it's called theoretical physics. Without funding for your so-called "research", it would forever remain so and we forever amount to little more than a fluke.

This is the kind of claim that's just funny to read - brushing off some of the smartest minds on the planet as lunatics and assuming their MO is to muck in the ultimate science fiction story just for kicks.

Thank you for shutting down the stupid "lol, science is a waste of money" garbage properly.

Having had many discussions on physics and black holes with my brother --- a professor of astrophysics specializing in supernova events and black holes -- I can assure you your question and your image make no sense.

A black hole is a collapsed star that is dense enough to trap light in a gravity well.

There is no magic of holes in the fabric of the universe, no time loops, no holes or loops in reality. They're just really big, super-dense stars, or multiple stars all collapsed together, and they operate with basic gravity

When it comes to cutting edge physics, theories are no longer so clear cut anymore. I have read a few physics journals, and your brother may be right, but the fact is even as one professor is proposing and trying to establish a new theory another is criticizing and picking holes in the theory. And a lot of times it is not so clear who is right without further data/observations

Even I picked several holes in Steven Hawking's documentary on space-time, and I was eventually proven right when another documentary by Neil Turok (Perimeter Institute) with some others physicists pick the same holes and aligning with my concussions.

What of physicist saying multi-verses (or alternatively a single infinite universe) means we would see our doubles . I can logically prove that that is complete rubbish, but thats off topic of OP

A black hole is a collapsed star that is dense enough to trap light in a gravity well.

There is no magic of holes in the fabric of the universe, no time loops, no holes or loops in reality. They're just really big, super-dense stars, or multiple stars all collapsed together, and they operate with basic gravity.

But how is it possible that gravity, the so called weakest force, can dominate over matter even at extreme state of matter. Consider an object falling to black hole accelerating over light speed before collapse with the attractor behind the horizont. If that collapse was to appear somewhere behind the horizont, and the matter being compressed by gravity, would it not overpower the gravity of the very mass itself?

My point is, that even an object with extremly small mass and thus small gravity, can create an event horizont around itself if it small enough, but would it , by accumulating mass, still keep itself "blackholing", what would mean that it would be so dense, that the mass with its gravity would overcome its own gravity by rest of the universal forces, should it not?

The most heavy and mass stars exist only for a blink of an eye (as short as 100 milions of years!), becouse their own big gravity cannot dominate over state of matter very compressed inside of it. While SMB's in centers of galaxies exist as long as the galaxy itself, so there must be some other stuff than just gravity of matter involved, I believe.

Gravity force

...

I'm not sure what it is you think you've plotted out there, but there's a reason why black hole physics is not part of high school curriculum. Since the link isn't immediately clear about it, a singularity is what you will find at the center of a black hole.

As far as "coordinates" go - you might be able to mathematically assign coordinates to a point "inside the volume" of a black hole when viewed from the outside, but once you start approaching a black hole, things stop adding up pretty darn quickly. Because under the force of gravity (of which you will have not shortage near a black hole) space starts to bend.

Feel free to work out all the math and submit it to a journal.

What you have written is nice from a simple perspective, but there are decades of research and study and measurements. Whatever you propose needs to fit at least a large portion of what has actually been measured.

And be prepared with a hard part of science: Whenever you go against something that has already been accepted, it is you who need to overcome the inertia and convince others that you are right.

I'm not saying it is right or wrong, only that this is probably not the best forum for it. Game developers include a lot of scientific-minded people, and we can usually smell basic scientific BS pretty easily, but if you think you have any scientific merit then a game development forum is the wrong place to discuss it.

Ok, it doesn't make sense from just the gravitational force, but this looks like what I thought just by tweaking initial velocity and coordinate of gravity source. I haven't tried altering the mass of the gravity source.

[edit] High gravity:

[edit] I think I just described orbit...

[edit] Seems like orbit, but who knows, it could describe some deep faucet of the universe.

Plus, given x = 1.8 t^2 / (0-x)^2 solving for x=-1 (which doesn't appear on the graph) gives t^2 = -1/1.8 => t = i sqrt(1/1.8), so who knows, maybe there's a 4th dimension.