formulaically, i understand the math. My question is more on the theoretical behaviour of something like a singularity.
How can something have zero volume but infinite density? How can something that don’t exist be infinitely dense?
Also, are all singularities the same and behave the same and have the same properties, regardless of the mass of the black hole?
For eg. A blackhole with 100 million solar mass vs another with 10 million solar mass. You take both mass, divide them by zero, and you get the same answer- infinite density.
Sorry for the juvenile question, maybe i shoulda posted this in nostupidquestions instead.
In: 1
It’s undecided if they actually exist.
A good rule of thumb, is that any time the word singularity is used, regardless of context, it means out models aren’t sophisticated enough to understand.
The word “singularity” comes from mathematics. It’s a place where a function’s behavior breaks down, and it stops behaving according to the rules that govern well-behaved functions.
If you ignore the effects of quantum mechanics, a black hole has zero size. Since mass is conserved, it must somehow collapse its initial mass into that zero size, and (finite mass) / (zero volume) = (infinity density). (More formally, you can think of the density as being the mass times the [Dirac delta function](https://en.wikipedia.org/wiki/Dirac_delta_function), which is how you get different infinite densities in some sense.) But it is not generally believed that this is actually the way the physics of real physical black holes works.
We don’t understand how quantum mechanics and gravity work together. (General) relativity and quantum mechanics make different predictions at extremely high energies and extremely small length scales, and of course the center of a black hole involves both. An understanding of what actually happens at the singularity depends on understanding how gravity works in a quantum-mechanical sense, and that is an active current area of research in physics with almost no known answers.
Note first that you exactly know the mass of any object just by how they bend spacetime. Also note that a “singularity” is not just the exact point where things go bonkers, but includes the behaviour around it; a singularity cannot exist on its own without the “non-singular” space around it. (Math talk: Formally, one would talk about the system of neighbourhoods of a point to formalize this in _stalk_-like manner.)
It is better to not think about black holes as points of infinite density of a fixed mass when trying to properly work with them. Instead, consider it as the spiky (i.e. singular) bump in spacetime itself. The mass-energy that caused it is represented and preserved in the bending it caused.
> Also, are all singularities the same and behave the same and have the same properties, regardless of the mass of the black hole?
Similar to elementary particles, black holes are determined by a small list of properties: mass, charge(s), and spin. In reality, black holes should usually be effectively uncharged, but of quite relevant mass and with spin. The same still holds true for the singularity itself, as long as you understand it as outlined in the first paragraph.
The idea is that the universe is a big ol’ grid and there is a “smallest distance” between each point on that grid. Nothing can move less than that distance except by not moving at all, and anything that is larger than zero is at least that distance across.
A singularity is a single point on this grid. Its volume is zero because all its dimensions are zero. If its volume is zero, and its density is anything that isn’t zero, then its density is undefined because it is divided by zero. In practice, this means its density is infinite if it isn’t zero.
… unless you subscribe to string theory, which allows no singularities as the smallest possible things are all at least one-dimensional, in which case you would call them black branes instead of black holes.
This is one of those questions, the ones where even simple answers tend to be highly technical. I will try to go straight to the point that answers your question without getting technical as soon as I pray to Richard Feynmann for assistance.
So, a black hole is created when the inward pull of gravity reaches the point where nothing for which we have any evidence can stop it from continuing to fall in until it reaches a mathematical point. On Earth, rocks and iron stop you from falling all the way to a mathematical point. With stars, it is fusion energy that stops you. With neutron stars, it is neutrons repulsing each other that stops this collapse.
But nothing prevents every bit of mass that falls in from falling all the way to the point that is the center of gravity. This point is infinitely small and thus has no volume.
Density is determined by mass and volume. The greater the mass, the greater the density, and the smaller the volume, the greater the density.
If any mass exists in a volume of zero, this means that the density is infinite.
We don’t actually know what the matter in a black hole looks like. We say it’s infinite density in no volume because that’s one way to interpret the math behind all of this. But it’s an attempt to interpret a mathematical function that no longer follows the rules of math. That’s what a mathematical singularity means – the math no longer works. Which is another way of saying we have no idea.
More modern interpretations think that inside of the Schwarzschild radius (the boundaries of the black hole that grows as its mass grows) is actually something like a ring of matter. This is because we’ve discovered that black holes actually have other properties, like charge and spin.
It’s undecided if they actually exist.
A good rule of thumb, is that any time the word singularity is used, regardless of context, it means out models aren’t sophisticated enough to understand.
The word “singularity” comes from mathematics. It’s a place where a function’s behavior breaks down, and it stops behaving according to the rules that govern well-behaved functions.
If you ignore the effects of quantum mechanics, a black hole has zero size. Since mass is conserved, it must somehow collapse its initial mass into that zero size, and (finite mass) / (zero volume) = (infinity density). (More formally, you can think of the density as being the mass times the [Dirac delta function](https://en.wikipedia.org/wiki/Dirac_delta_function), which is how you get different infinite densities in some sense.) But it is not generally believed that this is actually the way the physics of real physical black holes works.
We don’t understand how quantum mechanics and gravity work together. (General) relativity and quantum mechanics make different predictions at extremely high energies and extremely small length scales, and of course the center of a black hole involves both. An understanding of what actually happens at the singularity depends on understanding how gravity works in a quantum-mechanical sense, and that is an active current area of research in physics with almost no known answers.
Note first that you exactly know the mass of any object just by how they bend spacetime. Also note that a “singularity” is not just the exact point where things go bonkers, but includes the behaviour around it; a singularity cannot exist on its own without the “non-singular” space around it. (Math talk: Formally, one would talk about the system of neighbourhoods of a point to formalize this in _stalk_-like manner.)
It is better to not think about black holes as points of infinite density of a fixed mass when trying to properly work with them. Instead, consider it as the spiky (i.e. singular) bump in spacetime itself. The mass-energy that caused it is represented and preserved in the bending it caused.
> Also, are all singularities the same and behave the same and have the same properties, regardless of the mass of the black hole?
Similar to elementary particles, black holes are determined by a small list of properties: mass, charge(s), and spin. In reality, black holes should usually be effectively uncharged, but of quite relevant mass and with spin. The same still holds true for the singularity itself, as long as you understand it as outlined in the first paragraph.
The idea is that the universe is a big ol’ grid and there is a “smallest distance” between each point on that grid. Nothing can move less than that distance except by not moving at all, and anything that is larger than zero is at least that distance across.
A singularity is a single point on this grid. Its volume is zero because all its dimensions are zero. If its volume is zero, and its density is anything that isn’t zero, then its density is undefined because it is divided by zero. In practice, this means its density is infinite if it isn’t zero.
… unless you subscribe to string theory, which allows no singularities as the smallest possible things are all at least one-dimensional, in which case you would call them black branes instead of black holes.
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