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Gerard t Hooft Spinoza Institute, Utrecht University Utrecht University and

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The 4 Force Laws: Distance Force 1. Maxwell: 4. Gravitation: 2. Weak: 3. Strong:

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Gravity becomes more important at extremely tiny distance scales ! However, mass is energy...

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The highway across the desert Todays Limit … GUTs Planck length : Quantum Gravity LHC

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Planck Units

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The Black Hole Electromagnetism: like charges repel, opposite charges attract charges tend to neutralize Gravity: like masses attract masses tend to accumulate

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The Schwarzschild Solution to Einsteins equations Karl Schwarzschild 1916 Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

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The Schwarzschild Solution to Einsteins equations Karl Schwarzschild 1916 Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

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Universe I Universe II Time stands still at the horizon So, one cannot travel from one universe to the other Black Hole or wormhole?

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

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Stephen Hawkings great discovery: the radiating black hole

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

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Black hole plus matter Heavier black hole compare Hawkings particle emission process with the absorption process: In a black hole:

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of the final states time reversal symmetry (PCT): forwards and backwards in time: the same Probability = | Amplitude | 2 × (Volume of Phase Space)

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

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

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Dogma: We should be able to derive all properties of these states simply by applying General Relativity to the black hole horizon... [ isnt 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 !

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Region I Region II Horizon The quantum states in regions I and II are coherent. 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... space time

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Alternative theories: 1.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) 3.Information is in the Hawking radiation

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

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The physical description of the horizon problem...

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horizon Here, gravitational interactions become strong !! brick wall

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interaction horizon

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2-d surface

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Particles and horizons, the hybrid picture

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Black hole complementarity principle An observer going into a black hole can detect all other material that went in, but not the Hawking radiation An observer outside the black hole can detect the Hawking particles, but not all objects that have passed the horizon. Yet both observers describe the same reality

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Elaborating on this complementarity principle: An observer going into a black hole treats ingoing matter as a source of gravity, but Hawking radiation has no gravitational field. An observer outside the black detects the gravitational field due to the Hawking particles, but not the gravitational fields of the particles behind the horizon. Yet both observers describe the same space-time

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Space-time as seen by ingoing observer Space-time as seen by late observer outside

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This may be a conformal transformation of the interior region: Light-cones remain where they are, but distances and time intervals change! An exact local symmetry transformation, which does not leave the vacuum invariant, unless: (the conformal transformation)

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This local scale invariance is a local U (1) symmetry: electromagnetism as originally viewed by H. Weyl. Fields may behave as a representation of this U (1) symmetry. Is this a way to unify EM with gravity? The cosmological constant (Dark energy) couples directly to scales Is this a way to handle the cosmological constant problem? ???????? ???????????????

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

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Gravitational effect from ingoing objects particles out in

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The non-commucativity between and lleads to a Horizon Algebra : Also for electro-magnetism:

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The string world-sheet

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Black Hole Formation & Evaporation by Closed Strings

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

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y Black holes and extra dimensions x y 4-d world on D -brane Horizon of Big Hole Little Hole

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These would have a thermal distribution with equal probabilities for all particle species, corresponding to Hawkings temperature

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