The considerations below were inspired by a popular article related to the discovery of gravitational radiation in the formation of blackhole from two unexpectedly massive blackholes.
LIGO has hitherto detected two events in which the formation of blackhole as fusion of two blackholes has generated a detectable burst of gravitational radiation. The expected masses for the stars of the binary are typically around 10 solar masses. The later event involve a pair with masses of 8 and 14 solar masses marginally consistent with the expectation. The first event GW150914 involves masses of about 30 solar masses. This looks like a problem since blackhole formation is believed to be preceded via a formation of a red super giant and supernova and in this events star loses a large fraction of its mass.
The standard story evolution of binary to a pair of blackholes would go as follows.
Selma de Mink ( has proposed a new kind of story about the formation of blackholes from the stars of a binary.
- In the beginning the stars involved have masses in the range 10-30 solar masses. The first star runs out of the hydrogen fuel in its core and starts to burn hydrogen around the helium core. In this step it puffs up much of the hydrogen at its surface layers forming a red supergiant. The nuclear fusion proceeds in the core until iron core is formed and fusion cannot continue anymore. The first star collapses to a super nova and a lot of mass is thrown out (conservation of momentum forces this).
- Second star sucks much of the hydrogen after the formation of red supergiant. The core of the first star eventually collapses into a black hole. The stars gradually end end up close to each other. As the second star turns into a supergiant it engulfs its companion inside a common hydrogen envelope. The stars end up even closer to each other and the envelope is lost into space. Eventually the core of also second star collapses into a black hole. The two black holes finally merge together. The model predicts that due to the mass losses the masses of companions of the binary are not much higher than 10 solar masses. This is the problem.
What kind of story would TGD suggest? The basic ingredients of TGD story can be found in the article about LIGO discovery. Also the sections about the role of dark matter ant the magnetic flux tubes in the twistor lift of TGD might be helpful.
- The story begins with two very massive stars rotating around each other extremely rapidly and so close together than they become tidally locked. They are like tango dancers. Both dancers would spin around their own axis in the same direction as they spin with respect to each other. This spinning would stir the stars and make them homogenous. Nuclear fusion would continue in the entire volume of the star rather in the core only. Stars would never run out of fuel and throw away they hydrogen layers. Therefore the resulting blackhole would be much more massive. This story would apply only to binaries.
- The simulations of the homogenous model however have difficulties with more conventional binaries such as the blackhole of the second LIGO signal. Second problem is that the blackholes forming GW150914 have very low spins if any. The proposed explanation would in terms of dance metaphor.
Strong magnetic fields are present forcing the matter to flow near to the magnetic poles. The effect would be similar to that when figure skater stretches her arms to increase the moment of inertia in spin direction so that the spinning rate slows down by angular momentum conservation. This requires that the direction of the dipole differs from the axis of rotation considerably. Otherwise the spinning rate increases since moment of inertia is reduced: this is how the dancer develops the pirouette. The naive expectation is that the directions of the magnetic and rotation axis are near to each other.
- The additional actor in this story is dark matter identified as large heff=hgr phases with hbargr=GMm/v0, where v0/c< 1 has dimensions of velocity: (c=1 is assumed for convenience) (see this). M is the large mass and m a small mass, say mass of elementary particle. The parameter v0 could be proportional to a typical rotational velocity in the system with universal coefficient.
The crucial point is that the gravitational Compton length Λgr= hbargr/m= GM/v0 of the particle does not depend on its mass and for v0<c/2 is larger than Schwartschild radius rS= 2GM. For v0>c/2 the dark particles can reside inside blackhole.
- Could dark matter be involved with the formation of very massive blackholes in TGD framework? In particular, could the transformation of dark matter to ordinary matter devoured by the blackhole or ending as such to blackhole as such help to explain the large mass of GW150914?
I have written already earlier about a related problem. If dark matter were sucked by blackholes the amount of dark matter should be much smaller in the recent Universe and it would look very different. TGD inspired proposal is that the dark matter is dark in TGD sense and has large value of Planck constant heff=n× h =hgr implying that the dark Compton length for particle with mass m is given by Λ= hbargr/m= GM/v0=rS/2v0. Λgr is larger than the value of blackhole horizon radius for v0/c<1/2 so that the dark matter remains outside the blackhole unless it suffers a phase transition to ordinary matter.
For v0/c>1/2 dark matter can be regarded as being inside blackhole or having transformed to ordinary matter. Also the ordinary matter inside rS could transform to dark matter. For v0/c =1/2 for which Λ=rS holds true and one might say that dark matter resides at the surface of the blackhole.
- What could happen in blackhole binaries? Could the phase transition of dark matter to ordinary matter take place or could dark matter reside inside blackhole for v0/c ≥ 1/2? This would suggest large spin at the surface of blackhole. Note that the angular momenta of dark matter - possibly at the surface of blackhole - and ordinary matter in the interior could cancel each other.
The GRT based model GW150914 has a parameter with dimensions of velocity very near to c and the earlier argument leads to the proposal that it approaches its maximal value meaning that Λ approaches rS/2. Already Λ=rS allows to regard dark matter as part of blackhole: dark matter would reside at the surface of blackhole. The additional dark matter contribution could explain the large mass of GW150914 without giving up the standard view about how stars evolve.
- Could magnetic fields explain the low spin of the components of GW150914? In TGD based model for blackhole formation magnetic fields are in a key role. Quite generally, gravitational interactions would be mediated by gravitons propagating along magnetic flux tubes here. Sunspot phenomenon in Sun involves twisting of the flux tubes of the magnetic field and with 11 year period reconnections of flux tubes resolve the twisting: this involves loss of angular momentum. Something similar is expected now: dark photons, gravitons, and possibly also other parts at magnetic flux tubes take part of the angular momentum of a rotating blackhole (or star). The gamma ray pulse observed by Fermi telescope assigned to GW150914 could be associated with this un-twisting sending angular momentum of twisted flux tubes out of the system. This process would transfer the spin of the star out of the system and produce a slowly spinning blackhole. Same process could have taken place for the component blackholes and explain why their spins are so small.
- Do blackholes of the binary dance now? If the gravitational Compton length Λgr= GM/v0 of dark matter particles are so large that the other blackhole is contained within the sphere of radius Λgr, one might expect that they form single quantum system. This would favor v0/c considerably smaller than v0/c=1/2. Tidal locking could take place for the ordinary matter favoring parallel spins. For dark matter antiparallel spins would be favored by vortex analogy (hydrodynamical vortices with opposite spins are attracted).
See the article LIGO and TGD. For background see the chapter TGD and Astrophysics.