Entropy Bounds, Holography

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Entropy Bounds, Holography 2nd Law ( in
Cosmology )

• gr-qc/9904061PRL 84 (00)
• hep-th/9907032PLB 471 (00)
• with S. Foffa R. Sturani
• hep-th/9912055PRL 8? (00)
• with G. Veneziano

• Entropy bounds, holography, Causal Entropy
  Bound (CEB)
• Quantum Geometric entropies
• GSL

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BEB
Bekenstein 81
Entropy Bounds
R
S,E
Too much entropy/ too little energy gt GSL
(For systems of limited gravity RgtRg 2 E GN )
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Apply BEB to the universe ?! U is not a system
of limited gravity
Bekenstein 89
Entropy Bounds
Upper bound on curvature
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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 )
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Holographic entropy bound
But what is S ?
Holography
Bousso use light-sheets21D collections of
light-rays orthogonal to surface FS past ingoing
light-sheet- wrong! B 1. light-sheet of
decreasing area inside with converging
geodesics qlt0 2. Stop when qgt0 caustic
singularity need space-like projection
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CEB
R.B. Veneziano 00
Entropy Bounds
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Local form of CEB
Entropy Bounds
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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 lt RCC
Entropy Bounds
Find RCC use cosmological perturbations
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Comparison between entropy bounds
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Quantum entropy Entropy of quantum fluctuations
Modes freeze/ thaw exit / reenter
Quantum Geometric entropies
Quantum entropy is real ! So what about 2nd law ?
Constant !
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R.B., PRL 84 00
Proposed resolution
Proof in progress
Causal boundary has geometric entropy
Quantum Geometric entropies
Entropy bounds Geometric entropy dominates
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Generalized second law
R.B., PRL 84 00
G S L
In cosmology
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• Conclusions
• Holography modified by causality
• Singularity thms. modified by entropy bounds
• Hint shortest length scale