Geen diatitel

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Utrecht University
the Quantum structure
of the
BLACK HOLE HORIZON
Gerard t Hooft Berlin November 1, 2007
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paradox
Unitarity, Causality, ...
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The physical description of the difficulty
...
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Here, gravitational interactions become
strong !!
brick wall
horizon
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interaction
horizon
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By taking back reaction into account, one
can obtain a unitary scattering matrix
b
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Gravitational effect from ingoing objects
in
particles out
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Strategy infinitesimal modification of
in-state
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Repeat procedure
a string theory amplitude !!
nearly
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The string world-sheet
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Black Hole Formation Evaporation by
Closed Strings
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Horizon Algebra
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The Difference between
A black hole is a quantum superposition
of white holes and vice versa !!
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But, our algebra does not generate the
area law. Can we be more precise?
Transverse gravity?
Now, let us look at the contributions from
the Standard Model Scale
very late
in
out
very early
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It all happens at the origin of
Rindler Space
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The Standard Model Contribution to
the Horizon Algebra. I. The U (1) field
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The role of the Standard Models scalar
fields
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Scalar field acts as quantum hair
It generates a modification in the vector
field equations
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The average values of the scalar fields
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• Questions
• - What is the effect of Standard Model
  fermions ?
• - How do we handle non-Abelian vectors ?
• - What is the effect of the instanton
  angle ? ?
• - What modifications of the algebra are
  generated
• by the transverse grav. force ?
• Does this allow for a representation of
  the
• algebra with discrete states, as
  suggested by
• the entropy area law?

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A related question that we can answer What
is the effect of magnetic monopoles ?
N
S
arg has a Dirac string - ambiguity 2 ? n
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A non-Abelian gauge theory may now be
treated in its Cartan subalgebra, where the
diagonal components of electric and
magnetic charges are well-defined.
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Particles and horizons, the hybrid picture
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We intend to obtain the complete algebra
relating the in-operators to the
out-operators from whatever Standard Model
Lagrangian. Once the rules are clear, we
should be able once again to add
(transversal) gravity. The representation
of our algebra should then respect the
entropy / area law. The algebra should
generate the details of quantum black hole
dynamics.
part I The End
The black Hole Horizon as a Dynamical
System, Int.J.Mod.Phys. D15 (2006) 1587
earlier version gr-qc/0504120