Event horizon of a Schwarzschild black hole: Magnifying glass for Planck length physics

An attempt is made to describe the “thermodynamics” of semiclassical spacetime without specifying the detailed “molecular structure” of quantum spacetime, using the known properties of black holes. I give detailed arguments, essentially based on the behavior of quantum systems near the event horizon, which suggest that the event horizon of a Schwarschild black hole acts as a magnifying glass to probe Planck length physics even in those contexts in which the spacetime curvature is arbitrarily low. The quantum state describing a black hole, in any microscopic description of spacetime, has to possess certain universal form of density of states which can be ascertained from general considerations. Since a black hole can be formed from the collapse of any physical system with a low energy Hamiltonian H, it is suggested that the high energy behavior of any system should be described by a modified Hamiltonian of the form $H_{\mathrm{mod}}^2{=A}^2\ln {(1+H}^2{/A}^2)$ where $A^2\propto E_P^2.$ I also show that it is possible to construct several physical systems which have the black hole density of states and hence will be indistinguishable from a black hole as far as thermodynamic interactions are concerned. In particular, black holes can be thought of as one-particle excitations of a class of nonlocal field theories with the thermodynamics of black holes arising essentially from the asymptotic form of the dispersion relation satisfied by these excitations. These field theoretic models have correlation functions with a universal short distance behavior, which translates into the generic behavior of semiclassical black holes. Several implications of this paradigm are discussed.