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TGD based quantum explanation for the weird properties of Sagittarius A.

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Sabine Hosssenfelder tells about the weird properties of the giant blackhole at the center of Milky Way known as Sagittarius A* (briefly SA): see this. SA is located at a distance of 26,700 ly and has mass about 4.1× 1010 solar masses. Its Schwartschild radius rs= 2GM is 1.1× 1011 km. Note that astronomical unit (the distance of the Earth from the Sun) 1.49597870700× 108 km so that SA radius is almost 1000AU. The Schwartschild time Ts= rs/c is 41 s, about 2/3 minutes.

Hossenfelder lists six weird properties of SA.

  1. SA is silent, one might say dead suggesting that no matter is falling inside it. There is however an accretion disk around it.
  2. SA however shows signs of life by emitting periodically X ray flares bursting huge amounts of energy as a radiation. Blackhole should not do this unless it absorbs matter but it is not at all clear whether anything is going inside SA!
  3. SA is rotating extremely rapidly: the period τ of rotation is 10 minutes.
  4. SA possesses a dozen of planet-like objects, so called G-objects, rotating around SA with a velocity which is 60 percent of the maximal rotation velocity allowed by the condition that the rotation velocity inside the blackhole does not exceed the light velocity. How these objects can exist in an extremely hostile environment of the blackhole where the matter from outside should be flowing to the blackhole is a mystery.
  5. There is a blob of matter rotating around SA with a velocity, which is 30 percent of the velocity of light. The object periodically emits ray bursts, which might relate to the mystery of gamma ray bursts.

Could one understand these properties of SA by regarding SA as a blackhole-like object in the TGD sense consisting of a maximally dense flux tube spaghetti which is a quantum system with gravitational Planck constant ℏgr=GM/β0? Could one model SA as a quantum harmonic oscillator in the interior and using gravitational Coulomb potential in the exterior?

The reason for why matter is not falling inside SA could be the same as in the case of the hydrogen atom. Quantization would imply that the atom is a quantum system and does not dissipate so that the infrared catastrophe is avoided. Matter around it is at Bohr orbits of a central potential. The first guess would be Coulomb potential but also harmonic oscillator potential or something between these two could be considered.

  1. The quantization of angular momentum gives for a central potential and circular orbits r2ω= nGM/β0. The condition v2/r=ω2r= -d(GM(r)/r) holds true also for a central force. Recall that for the harmonic oscillator this gives ω=1/rs (c=1)and rn= n1/2r1, r1= rs/(2β0)1/2. The constancy of ω means that the system behaves like a rigid body. Note that one has n>0. Note that there is also an S-wave state, which corresponds to n=0 and can be described only by Schrödinger equations or its analog.
  2. For the Coulomb case one obtains ω=2/n3rs and rn= n2agr, agr= rs/2β02. In the interior, r1 ≤ rs requires β0≥ 1/2. In the exterior, agr≥ rs requires β0≤ 21/2 and r1≥ rs. This condition is not however absolutely necessary since the n>1 follows from the condition that the orbital velocity is smaller than c, as will be found. The conditions therefore fix β0 to the range [1/21/2,1/2,1]. The quantization β0=1/n would select β0∈{1/2,1} giving r1= (1,1/21/2)rs for the harmonic oscillator potential and rn∈ {2,1/2}n2rs outside the blackhole.
  3. Orbital velocities are given by vn= 2/nβ02 and vn2/β02, which is true for n> (2,4,8) for β0∈ {1,1/21/2,1/2}. The lowest allowed orbitals have radii (r3=9rs/2,r5= 25rs, r9=162rs).
  4. The inner radius of the accretion disk for which one can find the estimate rinner =30rs (see this). Inside the accretion disk, the harmonic oscillator model could be more appropriate than the Coulomb model. The inner edge of the accretion disk would correspond to (r8=32rs,r6= 36rs, r8=128rs) for β0∈ {1,1/21/2,1/2}. For β0=1/2 the prediction for the radius of the inner edge would be too large and also the prediction for β0=1/21/2 is somewhat too high.

Could one understand the findings about SA in this picture?

  1. The silence of SA would be completely analogous to the quantum silence of atoms. Furthermore, v The periodically occurring X-ray flares could be analogs of atomic transitions leading to the emission of photons. They could due to the internal excitations of the matter from lower to higher energy state. For β0=1 one has a maximal number of the harmonic oscillator states corresponding to the principal quantum number n=0,1,2 and the n=2 state would correspond to the horizon. Also transition to states which could be modelled as states in Coulomb potential are possible. n=3 Coulomb orbital would be the first allowed state β0=1. The prediction is that the total X-ray energy is quantized.
  2. Could one understand the rotation of SA in terms of the harmonic oscillator model predicting ω= 1/rs giving τ= 2π/rs. The estimated mass of the black hole gives τ= 4.2 minutes. Is the mass estimate for the blackhole too small by a factor of .42 or does the harmonic oscillator model fail?
  3. G-objects could be understood as gravitational analogs of the atomic electrons orbiting SA at radii with small values of n. The orbital radii are predicted to be proportional to n2. The allowed orbitals would correspond to {3≤ n≤ 8, n=5} for β0∈ {1,1/21/2} .
  4. The mysterious blob of matter rotating around SA with velocity v=3c/10 could correspond to a Coulombic Bohr orbit with a small value of n: n=6 orbit gives this value of the velocity for β0=1. For the other options the orbit would belong to the accretion disk.

To sum up, the β0=1 option is selected uniquely by the weird properties of SA.


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