Two neutron stars rotating rapidly around one another gradually lose energy
by emitting gravitational radiation. As they lose energy,
they orbit each other more quickly and more closely to one another.
What has been proposed here is that black holes do not form a singularity at their centre and that they cannot vary their angular velocity once formed. The proposal is fully in accord with Einstein's field equations and avoiding the creation of a singularity does avoid a number of other problems that have beset researchers in the area. However, it also leaves a number of questions unanswered. I may now be approaching a solution to many of them.
- Consider a Schwarzschild black hole onto which, more matter is falling. It is not enough to just accept that the black hole grows, layer by layer just like a hailstone. Somehow the matter must also distribute itself evenly over the surface. Imagine a pile of matter piling up at one point, possibly spreading out like treacle. The pile will be experiencing extreme pressure due to gravity; the same level of pressure as expected at the centre of a neutron star, Now in this situation, it is believed by some workers1 that the neutrons will enter a superfluid state. If this is correct, then spreading out to form a smooth shell would be expected to happen promptly. Once formed, a new event horizon can form, surrounding the last. Now, this can be easily extended to a rotating black hole but in this case, it is not just the shape but also the angular velocity at each point that has to match. This will normally leave a surplus amount of matter and angular velocity which will be discussed below.
- This accounts for matter; radiation is a different issue. But, from a distant viewpoint, the frequency decreases without limit and hence the wavelength increases without limit. In practice, one would expect this to be limited to the size of the black hole. What I would suggest, without any proper justification, is that it joins the superfluid neutrons to form what for now I refer to as quantum goo.
- To start with, consider an extremal black hole whose circumference moves at the speed of light. No further matter can be accumulated onto the surface. Matter, however, is still being attracted and will end up falling towards the event horizon. When close enough, it can form a superfluid which could spread out over the whole surface, if it were not for the conservation of angular momentum. To spread out, it needs to lose angular momentum, which it will do by radiating gravitational waves. If you follow a single unabsorbed particle, it will fall onto the surface at the equator and then spiral in toward one of the poles. any mass reaching a pole will have then have zero rotational energy but will have acquired. considerable polar momentum as it spiralled rapidly toward that point, leading to subsequent emission as a jet of matter. This needs to be backed up by a mathematical analysis which has yet to be successfully done. A sub-extremal black hole would achieve the same result but some of the matter would enshroud the black hole and thus enable growth; any surplus is ejected as a jet.
- There still remains an unresolved problem with black hole mergers. I remain unconvinced by the possibility, but the LIGO results do look impressive. At this stage, one needs to examine what is claimed: to claim that one has reached 5% confidence that the result is correct does not mean it trounces all other scenarios. It means that it is 95% more likely than an ensemble of all other possible results. I am probably expressing myself badly here but I am saying that a similar but non-identical solution could achieve the same or better match. So let us examine what to expect with the assumptions made here.
1 Rapid Cooling of the Neutron Star in Cassiopeia A Triggered by Neutron Superfluidity in Dense Matter
Page, Dany and Prakash, Madappa and Lattimer, James M. and Steiner, Andrew W
Phys. Rev. Lett. volume 106. issue = 8, pages = 081101-081105, 2011, Feb.