Squish

When discussing time dilation near Black Holes one normally refers to “local” time at the event horizon and remote time or “coordinate” time as experienced by a remote observer stationary relative the BH. But time dilation increases steadily as one approaches a Black Hole. For example, if the Black Hole event horizon radius is 1 million kilometers, then 1 kilometer away from the horizon the time dilation rate would be 1000:1 relative to coordinate time. At 1mm away it would be 1,000,000:1. It shoots up to infinity as one approaches the horizon. There is relative time dilation between any two places at different distances from the Black Hole.If you were falling feet first into a Black Hole, then as you approached the event horizon your feet would be very time dilated and slow down relative to your head. Your head would catch up with your feet and you would be concertinaed, go “squish”, and arrive at the event horizon as a thin pancake. In fact this would happen so fast that you would go “splat” as you pass through the event horizon. Of course the Black Hole would inevitably be rotating and would turn the splat into a smear. But for us distant observers, if we could make any observations that close to the event horizon, it would be a slow squish.This applies to any cloud of matter falling in. Leading particles would slow down relative to those further out, and in their local time they would all arrive together. However this is not quite true for a large mass because its trailing edge would slowly approach a new event horizon forming further out due to the added mass.All calculations for stellar collapse and for objects falling into Black Holes have ignored pressure in the collapsing medium. But with large amounts of matter falling into a Black Hole and “squishing”, pressure becomes an important factor. The pressure of the squish would force matter out sideways, but with matter falling in all around the equatorial regions of a Black Hole it has nowhere to go except out towards the poles. The extreme pressure would force a jet stream of matter poleward at tremendous speed (relativistic?) where it would all collide creating a jet of matter spewing outwards into space. I propose this as the mechanism behind the jet emissions observed in AGN galaxies, emitted by their central Black Holes.Now I just need some mathematical genius to do the Black Hole calculations taking pressure into account. Modern computers should help.I have had fun with my descriptive terms “squish”, “pancake”, etc, but I am sure there must be technical terms for these conditions, probably in the field of hydraulics.

Of course nothing takes place at the event horizon, at least as far as we distant observers are concerned. I envisage all this "squish" taking place a little distance outside the black hole. A lot of the matter squished out towards the poles would fall into the Black Hole before it got there, but the matter that did get there would collide with terrific force.

When a mass falls into a Black Hole, there is a Schwarzschild radius defined by the combined mass, and that radius only becomes an event horizon once all the incoming mass has fallen inside it. But due to time dilation the outer layers of that mass will approach the Schwarzschild radius asymptotically, forming a new event horizon after an infinite time.
I don't know how to copy a diagram into this reply, but it is illustrated perfectly in Liu and Zhang's "Exact solutions for shells collapsing towards an existing black hole", Physics letters 17/8/2009, in diagram 5b of that article.
Black holes merging is a little more complicated, but not relevant here.

Tasmypterix, It has been proposed that spaghettification might not take place as one falls in if the black hole is large enough and the gravity gradient more gradual. But I am suggesting that if the gravity doesn't get you, then the time dilation will. How these two opposite effects combine as one approaches the event horizon will depend on Black Hole size and your starting position and velocity. But the time dilation gradient goes to infinity at the event horizon, while the gravity gradient doesn't, so my squish effect will win out at the end.Regarding matter stopping at the event horizon, you have to get your head around the flow of time being different for different observers. Where there is mass, there is gravity, and where there is gravity time flows more slowly (relative to places with less gravity). But it is the gravity potential, not the force, that counts. Our clocks and all time here on Earth are slowed by Earth's gravity, and atomic clocks in GPS satellites up in orbit tick over a little faster than identical ones down here. NB. it all gets a bit more complicated when relative motion is also involved.Edited by Mike Holland, : Trying to avoid a future argument over a minor point..

OK, I had to do a bit of reading on the event horizons there. I couldn't find any estimates on the photon density in this hyper-photon sphere, their energy spectrum, or their anticipated half-life there before they either escape or fall in. I also have a gut feeling that polar orbiting photons will be pulled into equatorial orbits by the space drag, so that the result will be a ring of fire rather than a wall of fire.Anyway, it seems my pancake will be smeared as it gets cooked. Depends of the relative rates of timed dilation and space drag as one approaches the event horizon(s).But in the case of large amounts of matter (stars, clouds of gas) falling into a supermassive Black Hole at the center of an AGN galaxy, I think the squish would start taking place much further out, and my explanation for the polar jets is still viable.

OK, thanks, Paul. I didn't know there was a fairly well developed theory about the jets. I thought they were still a mystery. So I will scrap my theory and read the references you supplied.
Cheers, Mike

Paul, according to your Wiki reference,"Mechanisms behind the composition of jets remain uncertain."and according to your more detailed reference,"As was presented by J. McKinney, E. Blackman, and D. Meier at the conference (see also McKinney 2006; Meier, Koide, & Uchida 2000; Camenzind 2005), theorists are now concentrating on production of jets via differentially twisting magnetic fields tied to the ergosphere of the central BH. One of the primary difficulties is to get enough particles across the field lines so that the jet is more than just Poynting flux."So there is currently no real theory as to how the jets are formed. I am sticking to my story as a viable explanation, but need to think a bit more about the affects of space drag.I believe that there is a region a little way away from the event horizon where gravity, time dilation and pressure will interact to allow my mechanism to work and generate strong streams of matter accelerating towards the poles. I need a helpful mathematician to redo the old collapse calculations but including the effects of pressure. Liu and Zhang did the calculations for large massive spheres falling into a black hole, which is part of the solution, but they ignored spin and pressure. Their calculations did not show any spagettification, but only the outer parts of the spheres catching up with the inner parts as the inner parts were more time delayed.NB. Spin and space drag play an important part in my model. The space drag ensures that infalling matter is spread evenly all around the equator, which accounts for the squish all meeting at the poles so precisely.Edited by Mike Holland, : NB added.

Paul, has anyone ever done a calculation of simulation of an object falling into a black hole which shows spaghettification happening? The only one I know of is Liu and Zhang " Exact solutions for shells collapsing towards a pre-existing black hole", Phys letters 17/8/2009, and their calculations only showed the compression due to time dilation. Spaghettification sounds likely, but time dilation would win in the end because it goes up to infinity whereas gravity doesn't (not at the event horizon, anyway). (NB. Novikov slipped up in one of his books that I have, and claimed that gravity was infinite at the event horizon. )Has anyone ever calculated matter falling into a black hole and taken pressure into account?Mike

Really? And how do you spell cmb?I'm hardly going to start a research project. I completed a B.Sc in maths and physics in 1960 and then spent my life with computer software. I'm now 82, and Astronomy has been a hobby of mine since I was 14. So I need to find a kind mathematician who will do the calculations for me.I read a lot of science, and think a lot about it. I also follow the "frozen star" heresy and don't accept the black hole dogma. Not quite, anyway. But that's another story.

Actually I find forums unsatisfactory. I would like to sit down with an astrophysicist over a cup of coffee or three, and discuss these matters, but I don't know any astrophysicists. I tried emailing Saul Teukolsky, but he responded with some nonsense reasons for accepting the existence of black holes and then said he was too busy to continue the conversation.Even if I could do the mathematics, I could never get it published because I am not associated with any scientific or research institution.

Thanks for the offer, Anglagard. I will work out exactly what I would like calculated and write it up here, and make a note in August on my calendar.But I need to read up on Kerr black holes a bit more first.Edited by Mike Holland, : No reason given.