How Many Angels Can Sit on the Head of a Black Hole

The fundamental work of Bekenstein and Hawking on the thermodynamics of black holes gives us clues to a general theory of quantum gravity.  The most important of these is the Covariant Entropy Principle, which links Geometry and Quantum Mechanics: the logarithm of the dimension of the Hilbert space describing physics in a causal diamond in any space-time is equal, in the limit of large area, to one quarter of the maximal space-like area on the boundary of the diamond, measured in Planck units. This holds, in particular, for de Sitter space, which is the space-time our own universe will approach in the asymptotic future.  In that case the total dimension is finite. It was proposed by 't Hooft that all of the degrees of freedom describing a causal diamond live on that maximal area surface, and by Fischler and myself that excitations localized in the interior of the diamond correspond to constrained states of these boundary degrees of freedom.  The latter principle has profound implications for early universe cosmology and for the theory of supersymmetry breaking.  It leads to a mathematically finite theory of inflation and predicts the existence of supersymmetric partner particles in the multi TeV regime, possibly accessible to the LHC.