Gravitational Black Holes With A Twist And Supersymmetry

Ian E. Consterdine

2022 June 24

Introduction

The Standard Model of particle physics¹ is hugely successful and can be used to build objects to the density of neutron star degeneracy and possibly beyond in a quark-gluon plasma. Gravitational collapse, however, yields objects of yet higher density. When sufficient material exists within a given region – known as the Schwarzschild² or Kerr³ solution radius for non-rotating and rotating objects respectively – any escape from such an environ requires superluminal travel. As this is disallowed in physics, gravitational black holes with immense densities are the result.

As shown by Sir Roger Penrose in work that brought his 2022 Nobel Prize in physics, solutions to the Einstein equations of General Relativity theory yield unavoidable singularities – terms containing 1/r are singular as r → 0, i.e. at the black hole’s centre. Such singularities are anathema to physical evolution – “A point does not evolve” – Neil Turok, and must remain hidden from view if they exist at all. General Relativity theory appears to predict its own downfall.

It is expected that the rules of a Quantum Field Theory, QFT, of sufficient scope will rescue our understanding of physics from this current impasse and an improved understanding of quantum gravity will be the result.

Accordingly, a toy QFT that includes supersymmetry^{4, 5} – where each Standard Model particle has a supersymmetric partner such that the fermion and boson spin character is swapped – is shown to be a necessary and sufficient companion to General Relativity theory to make some progress.

As the star collapses from Chandrasekhar limits to beyond neutron star densities, it is proposed that the degenerate matter undergoes a transformation via the action of a quantum supersymmetry operator as the local spacetime distorts. The result is a black hole with the topology of a thin shell of invisible material. Gulp!

Building a shell from the inside of a solid ball

When a degenerate matter ball e.g. a neutron star⁶, undergoes further gravitational collapse beyond any quark-gluon plasma phase, it is suggested that Standard Model fermions, f, are converted to some supersymmetric counterpart bosons (sbosons, sb) due to metric curvature, tidal disruption effects and using the energy available in the collapse.

Although the mathematical machinery to encode these ideas in a working model was not immediately to hand, searches continued. Eventually, in early 2022, a treatment of the near-zone symmetries of Kerr black holes⁷ showed indirectly how further progress has been made. In that study it was shown how chiral boson generators are singular in the Schwarzschild limit and are not globally defined, as they do not respect the φ → φ + 2π periodicity. In other words, on approach to gravitational black hole horizons, the symmetric wavefunctions, Ψ, of bosons are maintained no longer. This result provides some critical theoretical support for the remainder of this post.

For chiral fermion generators, we suggest a similar distortion on antisymmetric wavefunctions to yield symmetric (bosonic) descriptors as the mechanism to supplement the supersymmetry operator Q defined in reference 5, lecture #6. The operator Q increases spin by 1/2 unit but maintains the in-bound fermion’s invariant mass whilst the dual operator Q decreases spin by 1/2 unit. Pauli exclusion⁸ on fermions does not apply to sbosons so there is no hindrance to the total number of conversions – the black hole event horizon grows in radius to match the increase in mass.

In summary, a soup of standard model fermions falling towards a black hole is twisted by the strong gravitational field and spun up by a supersymmetry operator to generate a condensate shell of massive sbosons – an effect of quantised gravity in 3 dimensions of space and 1 of time.

In Dirac notation this toy model QFT yields:

< Ψ_sb | Q | Ψ_f >

where the subscripts refer to fermion and sboson, respectively.

In the case of a non-rotating mass, a thin shell of sbosons develops with an inner radius at the Schwarzschild horizon. To a remote observer, light cones at this event horizon are oriented such as to point along the horizon (e.g. Sir Roger Penrose⁹) and the progression of time appears to stop – a clock’s next ‘tick’ is observed only at future infinity. Accretion of material from above the horizon causes the hole beneath the horizon to grow in size as more fermion to sboson conversions occur. Eventually, the horizon radius exceeds that of the degenerate matter ball as sboson wavefunctions condense onto the event horizon. Any outward, near-surface radiation emission from here onwards is some analytic continuation of Hawking radiation¹⁰ that will require a better understanding of this supersymmetric dark/invisible fraction of matter and its interactions.

Once the horizon radius is larger than the matter ball, a remote observer sees in-falling matter and radiation disappear from view at the event horizon. An in-falling observer’s experience is more extreme, however, as her fermions convert to sbosons with wavefunctions that spread out over the event horizon through the time evolution of Q: she is stretched, rent asunder, spun, splattered and spread out over the shell. The hitherto described process of spaghettification¹¹ is mild in comparison!

It is known that an object inside a shell of material feels no gravity from the shell itself¹² and any remnant degenerate matter remains trapped, floating below the horizon until after the shell shrinks due to Hawking radiation losses and evaporates completely. The largest black hole will not evaporate until a very, very long time has elapsed – of the order a googolplex, 10^10^100, years.

Incidentally, this process of conversion from a ball of degenerate matter to a shell of sboson matter explains how the surface area of the black hole and not its total volume¹³ is sufficient to describe its contents. This is because the contents have become the surface area: the horizon is the hologram of the original material having been passed through a gravitational + supersymmetric lens.

This description of gravitational black holes differs from that given hitherto because even though the mass/energy of the object as a whole may continue grow without limit until the background temperature falls below its own, it replaces non-physical singularities hidden behind event horizons, aka the cosmic censorship conjecture¹⁴, with invisible yet massive sboson shells at the locations of Schwarzschild/Kerr gravitational event horizons. Progress, eh?

As a further consideration we can envisage the observable universe as being within the confines of an ultra massive black hole as described by James Beacham in his presentation to The Royal Institute¹⁵. Accelerated universal expansion would then be a result of remote matter falling onto its event horizon and evaporating back to baryonic matter as it stwists and falls through the shell.

References and links

1. https://home.cern/science/physics/standard-model
2. https://en.wikipedia.org/wiki/Schwarzschild_radius
3. https://en.wikipedia.org/wiki/Rotating_black_hole
4. https://home.cern/science/physics/supersymmetry
5. “Spacetime & Quantum Mechanics, Total Positivity & Motives”, 2019, Nima Arkani-Hamed, Harvard Physics, https://www.youtube.com/watch?v=Sn0W_mwA7Q0 + playlist
6. https://imagine.gsfc.nasa.gov/science/objects/neutron_stars1.html
7. “Near-Zone Symmetries of Kerr Black Holes”, 2022, Lam Hui, Austin Joyce, Riccardo Penco, Luca Santoni and Adam R. Solomon, https://arxiv.org/pdf/2203.08832.pdf
8. http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html
9. For example – http://nrumiano.free.fr/Estars/int_bh.html
10. https://en.wikipedia.org/wiki/Hawking_radiation
11. https://en.wikipedia.org/wiki/Spaghettification
12. https://en.wikipedia.org/wiki/Shell_theorem
13. “The World as a Hologram”, L Susskind, https://arxiv.org/abs/hep-th/9409089
14. https://astronomy.swin.edu.au/cosmos/C/cosmic+censorship+conjecture
15. “The other end of a black hole”, J. Beacham, Royal Institute, October 2021 https://www.youtube.com/watch?v=A8bBhkhZtd8