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Entropy Bounds, Holography & 2 nd Law ( in Cosmology )

Ram Brustein. אוניברסיטת בן-גוריון. Entropy Bounds, Holography & 2 nd Law ( in Cosmology ). gr-qc/9904061=PRL 84 (00) hep-th/9907032=PLB 471 (00) with S. Foffa & R. Sturani hep-th/9912055=PRL 8? (00) with G. Veneziano. Entropy bounds, holography, Causal Entropy Bound (CEB)

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Entropy Bounds, Holography & 2 nd Law ( in Cosmology )

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  1. Ram Brustein אוניברסיטת בן-גוריון Entropy Bounds, Holography&2nd Law(in Cosmology) • gr-qc/9904061=PRL 84 (00) • hep-th/9907032=PLB 471 (00) • with S. Foffa & R. Sturani • hep-th/9912055=PRL 8? (00) • with G. Veneziano • Entropy bounds, holography, Causal Entropy Bound (CEB) • Quantum & Geometric entropies • GSL

  2. BEB : Bekenstein‘81 Entropy Bounds R S,E Too much entropy/ too little energy ==> GSL (For systems of limited gravity R>Rg=2 E GN )

  3. Apply BEB to the universe ?! U is not a system of limited gravity … Bekenstein‘89 Entropy Bounds Upper bound on curvature

  4. BEB is not compatible with QFT! QFT: Holography ‘tHooft ‘93 Susskind ‘95 Holographic principle: Any physical system can be completely specified by data stored on its boundary, without exceeding a density of one bit per Planck area. (adapted from Bousso hep-th/9911002 )

  5. Holographic entropy bound But what is S ? Holography Bousso: use light-sheets=2+1D collections of light-rays orthogonal to surface FS: past ingoing light-sheet- wrong! B: 1. light-sheet of decreasing area = “inside” with converging geodesics q<0 2. Stop when q>0 caustic ~ singularity need “space-like projection”

  6. £ S S s < 0 CEB t=0 CEB : R.B. & Veneziano ‘00 Entropy Bounds

  7. in cosmology: A bound on curvature (for RD FRW) CEB M P £ H , T N Local form of CEB : Entropy Bounds

  8. R3CC V R3CC R3CC Derivation of CEB : ( i )Entropy is maximized by the largest stable BH (s) that can fit in a region ( i i)The largest stable BH is determined by causality: BH horizon < RCC Entropy Bounds FindRCC : use cosmological perturbations

  9. limited gravity not limited gravity Bousso is o.k. Comparison between entropy bounds

  10. Quantum entropy: Entropy of quantum fluctuations Modes “freeze”/ “thaw” “exit” / “reenter” Quantum & Geometric entropies Quantum entropy is real ! So what about 2nd law ? Constant !

  11. R3CC V R3CC R3CC R.B., PRL 84 ‘00 Proposed resolution: Proof in progress Causal boundary has geometric entropy Quantum & Geometric entropies Entropy bounds: Geometric entropy dominates

  12. Generalized second law R.B., PRL 84 ‘00 G S L In cosmology:

  13. Conclusions • Holography modified by causality • Singularity thms. modified by entropy bounds • Hint: shortest length scale

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