Why is it assumed that singularities are at the center of black holes?

It is common to hear the terms black hole and singularity used interchangeably, but they are defined differently. A black hole is defined as a region of space from which nothing can escape, bounded by the event horizon. A singularity is an infinitely small region of infinite density at which point the mechanics of gravity break down.

The mathematics of singularities was used to theorize that black holes would exist in the universe. These black holes were found and identified, but this does not prove that they contain singularities.

A black hole must contain sufficient matter to create an event horizon, and this matter must be contained within its boundaries. These are finite boundaries, however, and thus there is no requirement for matter to be in an infinitely small space. The matter will not be at an infinite density, and thus there is not a singularity. Space-time is intact, Einsteins equations do not break down.

As a thought experiment, think about how a singularity could ever come to exist. How could matter enter a region with zero volume?

I believe the usual explanation is that the matter itself is annihilated so that only the gravitional field remains. The problem with your question is that there is a threshhold at which the internal pressure of highly compressed matter is no longer sufficient to support it. Degeneracy pressures will not support the structure if there is suffienct matter within a smal enough diameter, so it must collapse. The math is pretty solid. Many have tried to find ways to avoid what Eddington called "absurd behavior" but the consequences when a sufficiently large star can no longer support itself with heat from fusion processes are inevitable. It must collapse. And as it collapses, since gravity is related to radius, the gravitational field only gets stronger as the star falls inward on itself. It's important to understand (and not often pointed out) that it is the singularity from which nothing can escape. The event horizon is simply the distance from the singularity over which it retains that influence. It is only outside the event horizon that escape velocity drops below c.

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Well said, Thorkil2. I wish I had said that...

I could be wrong, but it seems obvious that the term 'singularity' as applied to black holes was derived from the concept of a mathematical singularity, which has been well-known and in use for probably hundreds of years. And it simply means the mathematics become UNDEFINED at that point. Though it may be described as such in popular science books, a black hole singularity is NOT some magical "point" that is "infinitely small" with "infinite density" and therefore "infinite spacetime curvature."

As noted in wiki, a singularity is not a thing.

Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the rate of change of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the Ultraviolet Catastrophe and in renormalization.

I prefer to think this, too, but of course we have no evidence to support this... or any position on the matter, so this is conjecture.

Actually, they do, as the Penrose-Hawking singularity theorems demonstrate.

Exactly. That would be ridiculous nonsense. A singularity is not a thing. It is simply an indication that the system within which one is working (in this case, GR) is incomplete.

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The singularity in a black hole is in the General Relativity equations (there is a location in the black hole where a lot of quantities diverge to infinity)--it is still possible that Quantum Gravity could eliminate the singularity. It's actually not the case that black holes come from singularity theory--they come from General Relativity, which also happens to put a singularity inside them.

Basically, the singularity is the place where we don't know what happens next, where another theory would have to come into play.

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Good article on an alternate theory in this month's Scientific American. Basically, the idea is that it may not be possible to get unlimited energy into a Planck volume because gravity becomes repulsive. Stay tuned, it's an interesting idea.

Sorry, thorkil2, that isn't right. Perhaps you had Hawking radiation in
mind, which involves matter/antimatter pair creation and annihilation.

Although I don't personally have a philosophical objection to matter
becoming infinitely dense at the center of a black hole, I see two
possible ways to avoid such an infinity, and both seem probable.

One is described by general relativity; the other by quantum mechanics.

As an expired star collapses, forming a black hole, the matter is
squeezed into a smaller and smaller volume. The density increases
without limit. That causes the curvature of spacetime (or gravitational
field strength) to increase without limit. That causes time dilation.
The time dilation means that the collapse occurs more slowly relative
to the outside universe than it would in a Newtonian universe. So the
matter is always falling toward the center, into a gravity well which
gets deeper and deeper, without limit, stretching farther and farther
in the radial direction. The deeper the gravity well gets, the greater
the spacetime curvature, which means the greater the time dilation.
Space turns into time in the radial direction. As matter falls closer
and closer to the center, the more space is converted to time. So
the matter can never reach the exact center-- it will be approaching
the center for all eternity, or until the black hole evaporates due to
Hawking radiation.

Quantum mechanics describes matter in a way limited by uncertainty.
The position and momentum of any chunk of matter cannot both be
described precisely. The matter is fuzzy. Given that we know the
matter is falling and thus must have some momentum, we can't say
precisely where it is. That would appear to limit the minimum volume
of the matter at the center of a black hole, even if there is no force
which can stop or even slow the collapse.

-- Jeff, in Minneapolis

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