Interesting point about the possibility that other forces may prevent complete contraction. It could also be fundamental principles in conjunction with forces, e.g., the well known uncertainty principle, that would by itself seem to forbid any â€œsharpâ€? singularity (meaning one that's well defined by any particular point inside the EH).
I was trying to imagine what it might be like inside an event horizon; wouldn't it be like a universe unto itself, sort of like an inverse of the one we're in (that is, swapping particles for empty space, and empty space for particles)? What's the speed of light on the inside of an EH?

[total crap]
Without any strong basis other than disliking infinities as unrealistic, I prefer the idea of an entirely new force. This would be repulsive and only of significant strength at really short range, say around the Planck length. It would be intimately linked with the Uncertainty Principle. I have often wondered why the resistance to localisation of energetic particles implied by quantum mechanics had not been labelled as a force.
Take a massive star, toward the end of it's nuclear burning options, as it contracts down to a smaller volume. Gravity never sleeps. The star goes through a series of phases of material type. It is initially 'atomic', with electrons whizzing around a nucleon core, but all are relatively discrete and separated entities that are loosely bound - it is gaseous. Then as a white dwarf it is becoming quite solid in nature with a vast lattice that electrons crowd jowl by cheek - a fluid of sorts. As density increases, the preference is for electrons and nucleons to combine giving a really dense solid stuff - the neutron star. Proceed further and you've folded space around it and formed a black hole. This yields an event horizon, but maybe doesn't require a singularity. Distant observers will be largely indifferent to what's inside, but not completely. If a new phase ( with this new 'Planck Force' ) kicks in and prevents the ultimate scrunch then the centre will have some non-zero width, and it's characteristics will be definable by experimental measurement of gravity wave behaviour as a probe of this region ( with inspirals say ). Why not? Black holes aren't totally one-way, they still inform the local surrounds via gravity. If the original star's mass is all at the centre then how do the gravitons get out to tap me on the shoulder later on after the hole formed? Since the event horizon is not a 'real' barrier but simply a region where/when the character of measurement changes ( in some respects time and distance interchange ) then there isn't any discontinuity.
You'd could also solve the black hole entropy issue. The core state type ( whatever becomes of matter under the Planck Force ) would preserve information in it's internal quantum states - much like any atom does with it's electron population distribution changing/spreading through available energy levels when it interacts. It remembers it's history...
Speaking of which, the Planck Force easily supplies the Big Bang without even leaning on higher dimensions for help... :-)
I suppose someone wants me to produce a numerical prediction now..... :-(
[/total crap]

Cheers, Mike.

( edit ) Then again the Planck Force might simply be what gravity looks like up close. The side we never saw before.....

The existance of a singularity may not actually violate uncertainty. Consider that a particle sitting at the singularity could have infinite momentum, but not move from that point due to the infinite curvature. This means that we could readily consider the uncertainty in momentum as infinite. Then, whether or not uncertainty holds is a question of looking at the limiting behavior in delta x and delta p.

There is an article in the New York Times, "Black holes collide and gravity quivers", covering LIGO and the NASA simulation but no mention is made of E@H.
Tullio

I can't help but be a bit annoyed, though, that they did not mention they were not the first to simulate orbits. That was done at Penn State. Anyway, to address some things that came up in this thread:

There's no mention of Einstein@Home because this source (binary black holes) makes a signal that E@H is not looking for. This signal lives a few seconds in the LIGO band, while E@H is looking for things that stay on (and whose frequency stays constant) for a long time. That means neutron stars (or other material compact objects) rather than black holes. It's not that they're ignoring E@H, it's just a different game.

If they're using the most popular mathematical setup these days, their simulations don't even contain the singularities.

There seems to be an idea around that a black hole is like a sphere, with the event horizon as the "surface" and the singularity as a little dot at the center. I've seen it in my students too, including one who is working on initial data for such simulations, so I think it's something we're primed to believe. But it's not like that.

The whole spacetime of a merging black hole binary is four-dimensional. Numerical relativity consists of taking a three-dimensional slice through it as initial data - that's the mathematical term for a "snapshot" of what the system is like at a particular time - and then evolving it. The snapshot on the next time slice is a little different, and so on and so on.

If the geometry were flat (Euclidean), it'd be like slicing through an apple where you'd always have to hit the core. But it's not flat, so there are ways you can slice it that avoid the singularities.

You can even slice to avoid the horizons, but just on that initial slice. They will show up on the next slice.

There is nothing magic about event horizons that says the laws of physics stop there. If you are going through, you don't notice anything unusual. One definition of the horizon is "nothing ever gets out," which means you would have to spend forever throwing stuff out and seeing what makes it to find out where the horizon was. And when you talk about dynamic situations it gets trickier - there are several types of horizon, which only coincide in the static case of a single black hole sitting there for all time.

But in general relativity, event horizons do imply singularities inside. The popular press often says the laws of physics break down there, but that's not true. In general you find a singularity (an infinite result) when some approximation you've been using to describe the system has broken down. General relativity implicitly makes the assumption that the quantum nature of spacetime can be ignored, and it's that assumption that is breaking down where general relativity predicts a singularity. In the last couple of years people have been calculating enough things with some versions of quantum gravity that they can see funny but finite behavior where general relativity predicts the singularity.

And when you talk about dynamic situations it gets trickier - there are several types of horizon, which only coincide in the static case of a single black hole sitting there for all time.

Types? Wow.....

Quote:

In the last couple of years people have been calculating enough things with some versions of quantum gravity that they can see funny but finite behavior where general relativity predicts the singularity.

Cool! Silly, but not singular? Hmmmm....

Thank you Ben. :-)
Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

## RE: RE: Interesting point

)

The existance of a singularity may not actually violate uncertainty. Consider that a particle sitting at the singularity could have infinite momentum, but not move from that point due to the infinite curvature. This means that we could readily consider the uncertainty in momentum as infinite. Then, whether or not uncertainty holds is a question of looking at the limiting behavior in delta x and delta p.

## There is an article in the

)

There is an article in the New York Times, "Black holes collide and gravity quivers", covering LIGO and the NASA simulation but no mention is made of E@H.

Tullio

## This is a neat

)

This is a neat simulation.

I can't help but be a bit annoyed, though, that they did not mention they were not the first to simulate orbits. That was done at Penn State. Anyway, to address some things that came up in this thread:

There's no mention of Einstein@Home because this source (binary black holes) makes a signal that E@H is not looking for. This signal lives a few seconds in the LIGO band, while E@H is looking for things that stay on (and whose frequency stays constant) for a long time. That means neutron stars (or other material compact objects) rather than black holes. It's not that they're ignoring E@H, it's just a different game.

If they're using the most popular mathematical setup these days, their simulations don't even contain the singularities.

There seems to be an idea around that a black hole is like a sphere, with the event horizon as the "surface" and the singularity as a little dot at the center. I've seen it in my students too, including one who is working on initial data for such simulations, so I think it's something we're primed to believe. But it's not like that.

The whole spacetime of a merging black hole binary is four-dimensional. Numerical relativity consists of taking a three-dimensional slice through it as initial data - that's the mathematical term for a "snapshot" of what the system is like at a particular time - and then evolving it. The snapshot on the next time slice is a little different, and so on and so on.

If the geometry were flat (Euclidean), it'd be like slicing through an apple where you'd always have to hit the core. But it's not flat, so there are ways you can slice it that avoid the singularities.

You can even slice to avoid the horizons, but just on that initial slice. They will show up on the next slice.

There is nothing magic about event horizons that says the laws of physics stop there. If you are going through, you don't notice anything unusual. One definition of the horizon is "nothing ever gets out," which means you would have to spend forever throwing stuff out and seeing what makes it to find out where the horizon was. And when you talk about dynamic situations it gets trickier - there are several types of horizon, which only coincide in the static case of a single black hole sitting there for all time.

But in general relativity, event horizons do imply singularities inside. The popular press often says the laws of physics break down there, but that's not true. In general you find a singularity (an infinite result) when some approximation you've been using to describe the system has broken down. General relativity implicitly makes the assumption that the quantum nature of spacetime can be ignored, and it's that assumption that is breaking down where general relativity predicts a singularity. In the last couple of years people have been calculating enough things with some versions of quantum gravity that they can see funny but finite behavior where general relativity predicts the singularity.

Hope this helps,

Ben

## RE: If they're using the

)

Wouldnâ€™t the behavior of the â€˜innerâ€™ boundary of integration place limits on the singularity?

## RE: I can't help but be a

)

Nothing done at pennstate really counts unless it's a drubbing on the football field delivered by the Panthers.

:-D

## RE: And when you talk about

)

Types? Wow.....

Cool! Silly, but not singular? Hmmmm....

Thank you Ben. :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal