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.

Published in IJGMMP, Improved version (misprints and typos corrected). 13 pages, one figure add and comments

References in corpus (2)

• Non-compact groups, Coherent States, Relativistic Wave equations and the Harmonic Oscillator
• Information metric from Riemannian superspaces

Cited by in corpus (3)

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• Black hole qubit correspondence from quantum circuits
• Charge dynamics and "in plane" magnetic field I: Rashba-Dresselhauss interaction, Majorana fermions and Aharonov-Casher theorems