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Strings 2009 @ Rome Holographic Neutron Stars

Strings 2009 @ Rome Holographic Neutron Stars. Erik Verlinde Work with Jan de Boer & Kyriakos Papadodimas. Why study Neutron Stars?. Black hole precursors. Most extreme form of matter. Holographic description of gravitational collapse: What is Space Time made of ?

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Strings 2009 @ Rome Holographic Neutron Stars

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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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