As for looking into a white hole in a dimensionless universe, the concept makes no physical sense.  A white hole can't exist in a dimensionless space.  Nor can any observer, to make such an observation.

I would imagine it to be an anti-hyperbolic geometry that an asymptote, so that all outwards directions eventually converge at a finite radius, and the white hole being a topological feature which counters this geometry, like how a circle in hyperbolic geometry forms an infinite room, the white hole being a region that has dimensions, and the volume permits non converging directions, but then when you pass the threshold (event horizon), all directions now lead away from the white hole and further into the anti-hyperbolic asymptotic space where they all eventually "run out of dimensions" and arrive at the same 0 dimensional location a radius away from the white hole.

Under a transformation that reverses the direction of time in the Schwarzschild metric, things which would be falling into black holes will instead fall out of them.

Ah! So a double or just entropic time reversal. Either the sequence of events are reversed or both sequence and direction is reversed. Where the math gives the reversed result. k, that makes sense. Except... wouldn't anything coming out of a white hole experience extreme anti-time dilation? The moment it leaves, wouldn't it age to almost infinity? But also... I suppose that would would also be accelerated close to the speed of light... So that might actually counteract the anti-time dilation, time would pass slower and faster for you. Talk about gamma ray central XD

"Negative" matter would be a source of antigravity, and produce a white hole instead of a black hole if you could bring enough of it (and if such stuff exists) into a small enough region of space to form an event horizon.  Same principle as forming a black hole, but with gravitational repulsion.

I can't imagine how one would obtain negative matter, as it would be like antimatter... but instead the entire universe is the wrong way around, and you'd need some tachyonic pair-production, how can someone even get a hold of imaginary light, or even a quantity of imaginary and anti-imaginary mass, and somehow reverse the direction of their products so that the negative matter formed is produced on the entropy forward side... Just imagine trying to even produce imaginary matter while standing on the real time axis, you'd need to somehow do something with imaginary time...I can barely comprehend what that would mean and do... It might just be easier to reverse entropy around an already existing black hole rather than attempt to make a white hole from scratch... Perhaps by somehow creating an alcubierre metric (already a problem) around a black hole, and well... turning it upside-down, if thats a thing? Or maybe the cheaty way; by creating a region of space with a very dense gas like Bose-Einstein condensate and create tiny pockets in it where their curvature is negative compared to the surrounding curvature, don't know if you'd be able to create a white hole with that...
Hmmm... would a white hole grow? I mean... would hawking radiation take place in reverse? Or would all those gamma rays coming out of a white hole make it shrink?

I would imagine it to be an anti-hyperbolic geometry that an asymptote, so that all outwards directions eventually converge at a finite radius, and the white hole being a topological feature which counters this geometry, like how a circle in hyperbolic geometry forms an infinite room, the white hole being a region that has dimensions, and the volume permits non converging directions, but then when you pass the threshold (event horizon), all directions now lead away from the white hole and further into the anti-hyperbolic asymptotic space where they all eventually "run out of dimensions" and arrive at the same 0 dimensional location a radius away from the white hole.

Both white holes and black holes have the geometry of the Schwarzschild metric, and both asymptote to Minkowskian space-time (the regular, flat space-time of special relativity) at large distances.  Observers far away from it have equal freedom to move in any of the three spatial dimensions.

Except... wouldn't anything coming out of a white hole experience extreme anti-time dilation?  The moment it leaves, wouldn't it age to almost infinity?

Nope!  Observers falling into a black hole do not "age to infinity" either.  The proper time they experience in the journey, whether it be into a black hole or out of a white hole, is quite short.  

The effect of the time dilation (which is the same as gravitational redshift) is that for observers outside a black hole, all events on the horizon take place an infinite time in the future.  They never observe anything cross the horizon.  And they never observe any events in the interior.  

For a white hole, this works the other way.  Observers outside the white hole see all events that transpired inside the horizon, because the light falls out of it.  Observers inside the horizon never see any events that occur outside the horizon, until they themselves fall out of it and reach a region where the light in the external universe is able to meet them.

The renditions on the webpage I linked earlier are again useful for visualizing this.

I can't imagine how one would obtain negative matter

Nor can I.

The renditions on the webpage I linked earlier are again useful for visualizing this.

They were extremely helpful! Although one part stated something curious... "“The” singularity is not a point. Rather, it is a 3-dimensional spatial boundary where general relativity commits suicide. New physics, presumably quantum gravity in some form, must replace general relativity at singularities. What that new physics is remains a profound unanswered question." So the singularity is not dimensionless? Maintaining all 3, and possibly 4, dimensions? This might be a very complicated question, but I would hope that there is a somewhat simple way to answer it, why is this? How does it maintain 3 dimensions and why would the singularity break relativity? What about it doesn't work out?

Hmmm... would a white hole grow? I mean... would hawking radiation take place in reverse?

Sorry for getting to this late, but I felt it warrants a deeper explanation worthy of a separate post.

White holes do feature Hawking radiation, which is observed in space-time analogues of white holes such as waves in fluid flow, acoustic holes, lasers, etc.  The nature of the radiation for the white hole is indeed a time reversal of the black hole.  

It is common to explain Hawking radiation in the language of entangled particle/antiparticle pairs splitting at the horizon, but I'm not a big fan of this explanation because it doesn't fully explain it and often causes confusions.  I will instead adopt the language of waves.  Specifically, the waves associated with the energy states of the quantum vacuum, which are what generate the particles of Hawking radiation near event horizons.

Near a white hole's horizon, vacuum oscillations with modes moving inward towards the the horizon will be blueshifted.  Think of waves trying to move against a current -- they get squashed together.

If there is no dispersion, then these waves will grow infinitely blueshifted and form a singularity on the horizon.  In this case the vacuum at the horizon of a white hole is highly unstable, and the white hole is destroyed.

If there is dispersion, then the modes of the vacuum oscillations separate.  Just as if you throw a rock into a pond and carefully watch the expanding ripples, you can see different wavelength surface waves spread apart at different speeds.  This dispersion has different and interesting consequences for the white hole horizon.  Some modes are superluminal and cross the horizon (analogous to quantum tunneling through the horizon), while others are subluminal and are dragged outward.

Thus, for a white hole with dispersion, observers outside the hole do observe Hawking radiation.  It emits radiation as if it has a temperature, just like with black holes.  However, the temperature will be negative, fitting with the idea of the white hole being a reversal of the arrow of time and entropy increase.

Theorists are quite sure that the vacuum modes behind Hawking radiation exhibit dispersion, but there is still much research into what the correct dispersion relation should be, and how it affects the horizon behavior.  This is also relevant for those studying effects of the horizons that show up in the Alcubierre metric (the leading horizon acts like a white hole, and the vacuum state there may be highly unstable and exhibit quantum effects that destroy the bubble or prevent it from becoming faster than light in the first place.

So the singularity is not dimensionless?

Aye.  This is unintuitive in the extreme.  For a Schwarzschild black hole, in the Schwarzschild coordinates, the singularity is at the point r=0.  In this sense, the singularity is zero-dimensional.  It is a point in the coordinates, and all paths inside the horizon will converge to that singularity point. 
However, those paths will not converge to each other!  As Hamilton explains on his site, infalling observers will get farther apart from each other even as they fall to the same point.  This is the tidal force in action.  The point of the singularity has infinite space-time curvature, and infinite curvature means infinite deviation of nearby geodesics.

It's analogous (not exactly the same, but a useful conceptual aid) as an "essential singularity" in complex functions.  A function near an essential singularity becomes very badly behaved, and if you take limits of different paths toward it, you can get all possible answers.  Or like how my favorite function, y=sin(1/x)/x, oscillates infinitely many times through an ever-increasing range of values of y, as you get ever closer to x=0.

why would the singularity break relativity? What about it doesn't work out?

Because general relativity is a classical theory, in the sense that the space-time is assumed to be continuous and infinitely differentiable.  It is expected that quantum mechanics should become relevant to the geometry on scales when space-time curvature becomes too large, like near the singularity.

Some modes are superluminal and cross the horizon (analogous to quantum tunneling through the horizon)

Sorry for my periodic flood of replies I have been giving in discussions. Anyways, it just hit me. If quantum tunneling can place a particle inside the horizon of a white hole, couldn't the same process place a particle outside of a black hole? Or is that just normal Hawking radiation and it is impossible to tunnel already existing particles outside it? (Just read this over again, maybe I am looking at this wrong, as a wave isn't quite a particle, idk though)

Thus, for a white hole with dispersion, observers outside the hole do observe Hawking radiation.

So if it loses mass, and already has negative mass, then it does grow?
I'll just throw these last few questions into this so you can answer with one post or something, don't want to flood this discussion topic . Is all the near black hole and inside black hole effects the same for a changing black hole? As in, a black hole that hasn't existed forever, and will not exist forever. And finally, is empty space a naked singularity? If I defined a singularity as some mass with a volume less than its schwarzschild radius, like 0. Then as I near 0 mass, maintaining the event horizon, soon it would become infinitesimal, and the even horizon would technically be radius 0, it doesn't exist. However there is a singularity, a massless, volume-less, singularity. Its hard to imagine a volume of empty space being an infinite amount of infinitesimal singularities... So I doubt that it would be a correct assumption, just interesting thought though...

If quantum tunneling can place a particle inside the horizon of a white hole, couldn't the same process place a particle outside of a black hole?

It's one way to think about it -- the semiclassical way of calculating Hawking radiation.  But the more rigorous/correct way is with properties of the quantum vacuum near the horizon.  The youtube channel PBS Space Time is currently working on an in-depth mini-series explaining it, so I suggest staying tuned to them.

So if it loses mass, and already has negative mass, then it does grow?

I'm not sure and I think it would depend on the dispersion relation.  I don't know of any rigorous solution for it offhand, other than in the case of no dispersion, where the white hole is rapidly destroyed by the vacuum instability at its horizon.  

a wave isn't quite a particle, idk though

  Just last week I demonstrated the double slit interference of single photons in my university's lab (and the data came out gorgeous), so I can confidently say that wave-particle duality is real.  Same is true for matter (matter waves).  They are both particles and waves, and which property you observe depends on the nature of the observation.

so I can confidently say that wave-particle duality is real.

I would not doubt the reality of wave-particle duality, however, it does get me thinking... If a particle is a wave, and a wave a particle, shouldn't it be neither? As in, if you define a particle as something that isn't a wave, and a wave not a particle, then wouldn't you be left with something that isn't a duality? For a duality implies that it is both, but thats like saying a photon is also a positron-electron pair, while it can act and be at times a positron-electron pair, that system has mass, and thus would act differently than what is always observed. So that either means if sometimes acts like a particle or sometimes a wave, never both at once... If it did, it would be neither. For if the former is how it is (being that it literally switches, then this would end there), but should it not... Being that it can in fact be both... Would we have something new? A particle wave, or a wave particle, being not a duality of both but a grey area in between?
On a side note, quantum mechanics is concerning me and I would like to see if you could ease these concerns, (hoping that I am wrong in my comparison), is quantum field theory a spoofed up version of the ether argument or is it not saying that the world is made up of a medium in which things flow, like waves through? It just feels like an argument implying that everything is part of fields, and interacts with them, is just as flawed as saying that things are particles... It is very unsettling to think we might, unintentionally, be bring back the ether argument. I'm hearing about stuff like gravitons and Higgs Bosons (the latter, I don't doubt its existence, just its implications), and it just feels wrong... A particle giving other particles mass makes no sense, a force carrier for gravity makes no sense... I could be saying that because I don't understand it... But for what I do understand, it becomes contradictory... Particles get their masses from being distortions, by changing time rate, you effectively get mass, being that the speed of light is the maxiumum or rather minimum time rate distortion. It seems that relativity already shows why mass is slower. Particles should not get their mass from another particle or field, unless we have extra dimensions that allow for different fundamental magnitudes to exist, particles, fundamentally, should be composed of spacetime, or rather a system of it... I don't know what that would imply, but I do know that the higgs field sounds like ether... String theory is right but also very wrong... Where it is right is the need for there being room to allow for the phenomena observed, however we don't need any extra spatial dimensions for this. What I do know... Is that in a 0-dimensional universe with only 1 particle... If we observed any more types or states of that particle, there must be a dimension to account for it... Otherwise we don't have enough room... Whether we already have enough spatial dimensions for some sort of unseen system that differentiates the states, that we have more in space or time, or perhaps an entirely new dimension of state... The problem still exists, there isn't enough room... And I am concerned that this has recreated the ether argument... Sorry for bringing up string and ether but I had to for this

I have what I hope is a simple question: the naked eye sky (i.e. down to 6th magnitude) contains some 3000 stars and a very few nebulae, clusters, etc. Does anyone know how to depict those naked eye stars volumetrically as they appear when you go outside and look up? I've seen plenty of 3D depictions of the local area of space from a 3D perspective, i.e. depicting the sun/solar system embedded in a volume of space with the nearby stars plotted in a 3D space, but I've never seen the sky you see when you go outside depicted volumetrically. It would be kinda tricky to depict since you'd have to devise some kind of foreshortening algorithm to approximate the depths encompassed by all of the 6th magnitude or brighter stars. Maybe use the stars to delineate a kind of topographic depth by creating isobars connecting stars that are the same distance from the earth? Perhaps embed stars of similar distance into the same "onionskin" layer that you could scroll through back and forth to get a sense of 3 dimensionality? Personally, I would love to see such a depiction of the naked eye night sky.....

If a particle is a wave, and a wave a particle, shouldn't it be neither? As in, if you define a particle as something that isn't a wave, and a wave not a particle, then wouldn't you be left with something that isn't a duality?

Particle-like properties include localization and collision/scattering.  Wave-like properties include diffraction, interference, and polarization.  These properties seem contradictory.  You would think that something which is a wave should not display the characteristics of a particle, and vice versa.  And yet by observation, nature is built from things that exhibit both behaviors.  

I can send light down a path with two slits, have it pass through both of them, interfere with itself as a wave on the far side, and then be received at a specific point on the detector as a particle.  I can do this for individual photons of light at a time.  

This is also not unique to light.  A good model for how electrons behave in electron orbitals is that they are waves oscillating around in the spherical potential well of the atomic nucleus.  In fact you can obtain exactly the same shapes as the electron orbitals by finding the harmonics of sound waves in a spherical cavity.  Electrons behave as waves.  And yet free electrons will impact targets or scatter off things just like particles.  Electrons behave as particles.

And it doesn't stop there.  We can show the same wave-particle duality for neutrons, and even large molecules.  The wave properties of bulk matter can be seen directly in Bose-Einstein Condensates.  Entire clouds of atoms interfere as waves.



How does nature decide whether an object shall behave like a wave or like a particle?  How does a wave which has passed through two slits and interfered with itself decide where it will impact the detector and be recorded as a particle strike?  These are essential mysteries of quantum mechanics.

On a side note, quantum mechanics is concerning me and I would like to see if you could ease these concerns, (hoping that I am wrong in my comparison), is quantum field theory a spoofed up version of the ether argument or is it not saying that the world is made up of a medium in which things flow, like waves through?

A bit of both yes and no.  It's subtle.

The luminiferous aether was the proposition that light, known to show wave-like properties, should have a medium in which it vibrates.  This is reasonable since all other waves travel through a medium.  The aether idea specifically modelled this medium in a Newtonian context, where there is some frame in which it is at rest, and so different observers with different velocities with respect to that medium should measure different velocities of light.

This prediction was falsified, by Michelson and Morley. They measured no change in the speed of light despite the changing motion of the Earth about the Sun.  (Aside:  This then led to the idea of "aether drag", where the Earth drags the aether with it so that light is always measured with the same speed.  But that then predicts that there should be no aberration of starlight, which was also falsified.  Actually, several more models for aether were developed after that, in much the same way as epicycles, to try to explain both the invariance of the speed of light and the aberration of light.  Again like epicycles, these models were designed to fit observations, but none were able to successfully predict new ones.  Finally the aether was put to rest with the development and experimental successes of relativity.)
  
However, this does not mean that light does not have a medium.  The vacuum is the medium!  Specifically, light is an oscillation of the electromagnetic field, and it obeys Lorentz invariance, meaning all observers measure the same speed of light. 

Then there is quantum field theory (QFT).  It is an extension of the paradigm of physics where nature is modeled by fields.  QFT treats every particle as a vibration of its respective field.  Every fundamental force is treated as an exchange of guage bosons -- the force carrier particles that govern those interactions.  This theory has a precise mathematical framework, and it makes exceptionally accurate predictions.  This paradigm of physics is enormously successful.

A particle giving other particles mass makes no sense

This model (The Higgs Mechanism) has been verified by experiment, for which the team won the Nobel Prize.  It may seem like it makes no sense, but it correctly describes and predicts nature!

I could be saying that because I don't understand it...

Try watching PBS Space Time's explanation.
[youtube]kixAljyfdqU[/youtube]

Particles should not get their mass from another particle or field, unless we have extra dimensions that allow for different fundamental magnitudes to exist

Not extra dimensions.  Extra fields.  There's no need for more than the 3+1 dimensions of space-time.  You don't need extra dimensions to have an electromagnetic field, do you?  The other fields are no different.  They just assign a value of that field to every point in space time.

The appearance of additional dimensions in string theory is merely a mathematical hack to avoid internal contradictions.  I have no idea if string theory is a valid model of nature or not.  It isn't currently testable.

And I am concerned that this has recreated the ether argument... Sorry for bringing up string and ether but I had to for this

You're doing fine, though consider formatting your posts with paragraphs to help make them more readable.  Questions are welcome, especially questions whose purpose is to try to understand things which are genuinely confusing!  The goal is to understand nature better.  I hope these answers help at least a little.

Wasn't sure if it would be best to post this here or make a new thread or if its even the proper forum to put this in (not even to mention thread) but are there any sites or software by which I can find the characteristics of compounds and mixtures and the such by giving, say, a formula, and vice versa (by giving characteristics I want to figure out what has), these characteristics being things such as color, phase change points/diagrams, and possibly the ability to figure out how this particular element or compound could exist in a certain enviorment? I'm sure this is the equivalent of asking if I can find a program to simulate the entire universe accurately on my PC but I mean, it's not perfect but SE does a pretty good job of that so I figured why not ask. I want to be able to create planets, whether in SE or in other programs, that have at least semi-realistic surface compositions rather than "lots of iron" "lots of silicates" "lots and lots of carbon, woo hoo graphite" which is basically all I can do at the moment without being unsure of the realism of that actually occurring. I mean, I'm sure it would be super hard (probably impossible without some insanely advanced tech) to find, say, a planet with a whole atmosphere of iodine, which would result in purple skies (or am I totally wrong about that? Nitrogen and oxygen are colorless, unless you cool the oxygen down into a liquid state, so...does gas color not effect atmosphere color, and/or is blue sort of the "defaut" color when 99% of the gasses present are colorless?) but it may or may not be possible. I don't know, and thats the point: I want to be able to know if such situations could exist, why/how, and I can figure out from that result how common that might be and if I should include it in a system I make or something. And no, if there are none out there, don't tell me to develop one; I know nothing of coding beyond the very, very basics and would probably have a hard time building a program that would even work. 

Also, if there is no single software/site that can do this, are there any that I could use in tandem with each other to achieve the same result? I don't mind using multiple things if it means I can make sure the stuff I make is at least pretty realistic. If theres none out there at all, well, I guess I'll just have to keep taking shots in the dark and making my best semi-educated guesses, and thanks for the help anyway...

Ps, sorry for the wall of text. I explain things way beyond the necessary amount and- ugh, sorry, doing it again. 

Sounds like you'll need to do a little qualitative stoichiometry with a Vapor Fractometer or a gas chromatograph to build a data base on the characteristics you want. It's kind of like predicting the folding of proteins, just way too many factors that make up all of its qualities. For example, Methyl anthranilate IS the flavor or grape. It was accidentally discovered and used in food production before it was discovered in the real fruit of grapes. I'm also a fan of the Rare Earth theory: http://blogs.discovermagazine.com/d-bri ... omPB5dME0M

The Meat & Potatoes article: Terrestrial planets across space and time.
https://arxiv.org/abs/1602.00690

are there any sites or software by which I can find the characteristics of compounds and mixtures and the such by giving, say, a formula,

Unfortunately there is no site or formula that will do this.  Calculating the physical properties of arbitrary substances is hard.  Calculating it for a particular substance from first principles can be worthy of a research paper.  For solids you must model how energy is stored in vibrational modes of the structure, as well as account for the quantization of those modes (vibrations can't have arbitrary energy), and the behavior of the electrons.  For liquids and gases you must model their degrees of freedom and intermolecular interactions.  Long story short, it's reasonably doable for some substances, but to produce formulas that generalize to all systems is effectively impossible.  Better to look up the properties in a table as determined by experiment, like Gnargenox says.

Also, if there is no single software/site that can do this, are there any that I could use in tandem with each other to achieve the same result?

Probably the closest thing that exists for doing what you want is in fact Space Engine.  It doesn't "simulate" the universe so much as "emulate" it, and it does so as accurately as possible with the knowledge of physics and astronomy available.  Its accuracy also continues to improve over time.  I really don't think there's much else out there that is better or more complete for showing what is or is not possible to exist in the universe.

This model (The Higgs Mechanism) has been verified by experiment, for which the team won the Nobel Prize.  It may seem like it makes no sense, but it correctly describes and predicts nature!

My problem with it is that it both is unnecessary and unreasonable. If particles were to "naturally" be "trying" to move at the speed of light, but their fields are interacting with the Higgs Field, "slowing" them down, it would have to be absorbing an infinite amount of energy. To say it "just does that" feels wrong.


Here is a possible way to describe mass and everything without invoking fields. Lets just say that there is something called a "time rate" which effectively is the rate of time which passes for a system described. Now lets propose it has two components, your local time rate (which is the rate in time in your general location dependant on the curvature of spacetime) and then a multiplier. This multiplier changes the maximum time rate away from its "0-value" (effectively light speed), this is dependant on "mass". Kinda like a time drag (but with a medium being spacetime and without a field). This decreased time rate for this particle effectively acts as a gravitational field, which can be used to calculate its mass. All of the particle's properties, along with its mass, can be described in a way that is no different from saying its one particle or another. For if you place an electron and a positron next to each other, or any other particle, but no time passes, they effectively are massless, and no different from each other. Particles get their identities and properties by the paths they trace through time in systems, being part of its own identity as much as it is the name of the particle, like a shape. I don't know why only certain energy quantities and system arrangements would only be stable for a handful of particles rather than a bunch, probably thats where the quantum stuff kicks in. But thats so far what I have, which would not require a Higgs Field Medium.


Heres an abstract one... Is it possible (rather, allowed) for me to describe nothing as a particle? As in... Could I say a nothing-on is a massless particle, with some spin number which it looks the same no matter which direction you look at it, has no charge, and perhaps some other properties... Maybe saying that it can carry certain energy levels that equates to certain particles being in that location, it can (like a photon) have a type of mass that allows for it to be considered as a singularity under the right conditions, and so on?


And one final one... Would the real volume of a black hole be smaller than that which is found using the schwarschild radius? As in, if we just consider that the volume an event horizon takes up, just from the schwarschild radius, we would just find the "euclidean" volume. But if we consider volume, not the space the black hole takes up, but rather the actual volume inside the black hole. Would it be less than or more than the euclidean volume. To clarify, volume, being the amount of space that can be moved through, and which the distance between each point is measured in the same scale of unit, being that spacetime is warped, how does this affect the internal volume?

My problem with it is that it both is unnecessary and unreasonable.

It was theorized as a solution to an outstanding problem in the standard model, and it was verified by experiment.  That's as close to necessary and reasonable as anything gets.

In science it is not justifiable to dismiss an experimentally verified model just because you think it doesn't make sense.  I don't mean for this to sound condescending, but what's more likely is that you don't understand it at a sufficiently technical level to be able to make sense of it.  Neither do I, for that matter!  I have not studied the Higgs Mechanism formally and much of it goes beyond my comprehension.  My understanding is probably about as good as yours.

Is it possible (rather, allowed) for me to describe nothing as a particle?

You can attempt to construct any type of model that you want.  That is the joy of theorizing.   But if you want confidence that your model usefully and accurately describes nature (and especially if you want to convince other people that it is useful and accurately describes nature), then it must meet the following criteria:

1)  It must be mathematically rigorous such that it makes specific, potentially falsifiable predictions.
2)  Those predictions must then be verified by experiment. 

Would the real volume of a black hole be smaller than that which is found using the schwarschild radius?

Possibly unexpected answer:  There is no real value for the volume enclosed by the event horizon of a black hole!  It is not an invariant quantity.  

If you recall from special relativity that simultaneity is relative, this means that different observers have different notions of what constitutes a simultaneous slicing of the space-time.  They will have different definitions for "constant time" slice with which to define the volume enclosed, and for a black hole they will yield different answers.  It may even be zero!

So this particular question does not have a meaningful answer.  (Rather, the answer is a good lesson on principles of relativity).  That might be unsatisfying, because I think the motivation for your question is to understand how the curvature affects common geometric properties like volume.  So let me reframe your question to try to help.  It turns out that although the volume enclosed in a black hole is not invariant, the surface area of the event horizon is!  (The event horizon is a null surface, so it is invariant to space-time transformations and all observers agree on its value).

The horizon area of a black hole is 



Notice that 2GM/c² is the Schwarzschild radius.  So this is exactly the same formula as the surface area of a sphere using the Schwarzschild radius.  This might make you think that the space-time curvature hasn't changed the properties of the space from that of Euclidean geometry.  Do not be deceived!  

Recall from the earlier discussion of "reduced circumference" that the radial coordinate r in Schwarzschild geometry was defined such that the circumference at that radius is 2πr.  But if you measure direct distances between different radii, they will disagree with your intuitions from Euclidean geometry.  

That, I think, is the clearest way to see the effect of the curved geometry on the space.  There is more radial distance between nearby spherical shells around a black hole than you would think from the Schwarzschild coordinates.

The existence of singularities haven't been and can't be confirmed by experiments, I believe. It's a mathematical convenient way to express what we see from the outside, but physically it's hard to say what exactly exists within a black hole. Or?