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BLACK HOLES

Utrecht University. on. BLACK HOLES. Gerard ’t Hooft Dublin November 13, 2007. CERN. LHC Large Hadron Collider. *. *. 7 TeV + 7 TeV. Planck length :. Today’s Limit …. LHC. Quantum Gravity. The highway across the desert. GUTs. The Universal Force Law:.

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BLACK HOLES

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  1. Utrecht University on BLACK HOLES Gerard ’t Hooft Dublin November 13,2007

  2. CERN LHC Large Hadron Collider * *

  3. 7 TeV + 7 TeV

  4. Planck length : Today’s Limit … LHC Quantum Gravity The highway across the desert GUTs

  5. The Universal Force Law: Maxwell & YM: Force Gravitation: Distance

  6. General Relativity

  7. Gravity becomes more importantat extremely tiny distance scales ! However, mass is energy ...

  8. Planck Units

  9. P P P P P P P P photon graviton P P P P P P P P The Photon The Graviton Spin = 2 Spin = 1 Equal masses attract one another ... Equal charges repel one another ...

  10. Moon Moon Moon Sun Force and spin strength of force Earth This is the wave function of a spin 2 particle Graviton

  11. The Black Hole Electromagnetism: like charges repel, oppositecharges attract → charges tend to neutralize Gravity: like masses attract → masses tend to accumulate

  12. horizon Where is the gravitational field strongest?The formation of a Black Hole Black Hole even light cannot escape from within this region ...

  13. The Schwarzschild Solution to Einstein’s equations Karl Schwarzschild 1916 “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”

  14. The Schwarzschild Solution to Einstein’s equations Karl Schwarzschild 1916 “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”

  15. “Time” stands still at the horizon So, one cannot travel from one universe to the other Black Hole Universe I Universe II

  16. As seen by distant observer As experienced by astro- naut himself Time stands still at the horizon Continues his way through They experience time differently. Mathematics tells us that, consequently, they experience particles differently as well

  17. Stephen Hawking’s great discovery: the radiating black hole

  18. horizon Region I Region II negative energy positive energy

  19. While emitting particles, the black hole looses energy, hence mass ... they become smaller. Lighter (smaller) black holes emit more intense radiation than heavier (larger) ones The emission becomes more and more intense, and ends with ...

  20. 12 12 3 3 9 9 6 6 Heavier black hole In a black hole: compare Hawking’s particle emission process with the absorption process: →Heavier black hole Black hole plus matter

  21. If the heavier black hole could exist in much more quantum states than the lighter one, the absorption process would be favored ... If the heavier black hole could exist in much fewer quantum states than the lighter one, the emission process would be favored ... Comparing the probabilities of these two processes, gives us the number of quantum states !

  22. of the final states time reversal symmetry (PCT): forwards and backwards in time: the same

  23. The black hole as an information processing machine The constant of integration: a few “bits” on the side ...

  24. Entropy = ln ( # states ) = ¼ (area of horizon) Are black holes just “elementary particles”? Are elementary particles just “black holes”? Imploding matter Hawking particles Black hole “particle”

  25. Dogma: We should be able to derive all properties of these states simply by applying General Relativity to the black hole horizon ... [ isn’t it ? ] That does NOT seem to be the case !! For starters: every initial state that forms a black hole generates the same thermal final state But should a pure quantum initial state not evolve into a pure final state? The calculation of the Hawking effect suggests that pure states evolve into mixed states !

  26. Horizon The quantum states in regions I and II are coherent. Region II Region I This means that quantum interference experiments in region I cannot be carried out without considering the states in region II But this implies that the state in region I is not a “pure quantum state”; it is a probabilistic mixture of different possible states ...

  27. Alternative theories: • No scattering, but indeed loss of quantum coherence • (problem: energy conservation) 2. After explosion by radiation: black hole remnant (problem: infinite degeneracy of the remnants) • Information is in the Hawking radiation

  28. Black Holes require new axioms for the quantization of gravity How do we reconcile these with LOCALITY? paradox Black Hole Quantum Coherence is realized in String/Membrane Theories ! -- at the expense of locality? -- How does Nature process information ? paradox Unitarity, Causality, ...

  29. The physical description of the difficulty ...

  30. Here, gravitational interactions become strong !! brick wall horizon

  31. interaction horizon

  32. By taking back reaction into account, one can obtain a unitary scattering matrix b

  33. Black Hole Formation & Evaporation by Closed Strings

  34. WHITE HOLE BLACK HOLE The Difference between A black hole is a quantum superposition of white holes and vice versa !!

  35. Particles and horizons, the hybrid picture

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