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Exploring Neutron Stars: The Holographic Description and Gravitational Collapse Phenomenon

This study delves into the intriguing aspects of neutron stars and their holographic description in gravitational collapse scenarios. Covering topics such as black hole precursors, degenerate fermions, and the Oppenheimer-Volkoff Limit, the research by Erik Verlinde, Jan de Boer, and Kyriakos Papadodimas raises fundamental questions about space-time and the nature of matter. Through the AdS/CFT correspondence, the operator-state relationship provides insights into strong coupling behaviors and fermionic particles in the bulk. The analysis explores composite operators, Fermi levels, and the dynamics near the OV limit, indicating potential phase transitions and tachyonic modes. This investigation sheds light on the gravitational collapse dynamics and the role of interactions before critical thresholds are reached.

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Exploring Neutron Stars: The Holographic Description and Gravitational Collapse Phenomenon

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  1. Strings 2009 @ RomeHolographic Neutron Stars Erik Verlinde Work with Jan de Boer & Kyriakos Papadodimas

  2. Why study Neutron Stars? • Black hole precursors. • Most extreme form of matter. • Holographic description of gravitational collapse: • What is Space Time made of ? • (David Gross: 1st new question ) • ......................and it is fun!

  3. Neutron Star Neutron Starsin a Nutshell Degenerate Fermions Typical mass “astrophysical see saw formula”

  4. Oppenheimer-Volkoff Limit

  5. AdS/CFT : operator-state correspondence 

  6. “” Fermionic single trace operators r = odd like => Strong coupling obey fermi statistics behave as free fields forN  and correspond to a fermionic particles in the bulk

  7. What is the operator with the lowest dimension  found in the factorization |xi|  0 and |yj|   ? Note that for N  Wick’s theorem gives:

  8. _ Composite Operators N-particle states correspond to composites defined by In each step the total mass increases by the amount => fermi energy: increasing function of particle #

  9. Composite Operators at infinite N out of two fields out of d+1 fields or (d+1)(d+2)/2 fields

  10. Total # of particles: Degenerate Composite Operators nF = # of “shells”= “Fermi level” . # of particles in the n-th shell: nF 3 2 1 0

  11. AdS description at infinite N = one particle state with wave function and energy Multi-trace operator = Slater determinant

  12. Trapped Cold Fermi Gas in AdS F

  13. Hydrodynamic (or “astrophysical”) limit Together withN  we take keeping Partial ‘t Hooft suppression: n-point functions vanish, except those that are sufficiently enhanced by combinatorical factors. Most bulk interactions are still suppressed, except gravity. Note: # of particles is infinite => classical fluid.

  14. M particle # log m

  15. Hydrodynamic description Free degenerate Fermi gas: Particle & energy densities Determined by chemical potential

  16. => Tolman The edge of the star r = R is reached when Fermi energy of boundary CFT For a metric of the form conservation of energy momentum implies

  17. Mass and Particle Number = ADM mass

  18. Pure AdS exactly matches CFT M particle # log m

  19. Self Gravitating Neutron Star Metric Ansatz + Einstein equations + Stress energy conservation “TOV equations”

  20. M log (0) log m

  21. Neutron Star near OV limit

  22. M particle # log m

  23. Thermodynamic relations in the CFT At OV limit # of states at Fermi surface diverges. Assuming extensivity the CFT pressure obeys: Clear sign of an instability: phase transition.  

  24. dF/dN log m N=particle #

  25. What happens beyond the OV limit? • A tachyonic mode develops leading to gravitational collapse. • Essential phenomenon happens at center => infrared in CFT. • Signal of a high density phase transition in the CFT. • Can one find more precise bounds on the other interactions. • Do they play some role before the collapse? • Can one study the dynamics of the collapse in the CFT Concluding

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