Quantum Gravity: physics from supergeometries

Abstract

We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the literature. To this end, an emergent metric solution obtained previously in [Physics Letters B 661, 186-191 (2008)] from a particular non-degenerate Riemmanian superspace is introduced. This emergent metric is described by a physical coherent state belonging to the metaplectic group Mp (n) with a Poissonian distribution at lower n (number basis) restoring the classical thermal continuum behaviour at large n (n ! 1), or leading to non-classical radiation states, as is conjectured in a quite general basis by mean the Bekenstein- Mukhanov effect. Group-dependent conditions that control the behavior of the macroscopic regime spectrum (thermal or not), as the relationship with the problem of area / entropy of the black hole are presented and discussed.