Nonunitary HD gravity classically equivalent to Einstein gravity and its Newtonian limit

TL;DR

This paper introduces a nonunitary extension of fourth order gravity that is classically equivalent to Einstein gravity, predicts a transition from quantum to classical behavior at macroscopic scales, and offers insights into black hole entropy and singularity regularization.

Contribution

It proposes a nonunitary gravity model with doubled matter operators, connecting classical Einstein gravity to quantum collapse phenomena and black hole entropy.

Findings

Avoids runaway solutions via matter operator doubling

Predicts a quantum-classical transition at 10^{11} proton masses

Provides a trans-Planckian regularization of collapse singularities

Abstract

Runaway solutions can be avoided in fourth order gravity by a doubling of the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with the change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its non-unitary Newtonian limit is shown to lead to a sharp transition, around $10^{11}$ proton masses, from the wavelike properties of microscopic particles to the classical behavior of macroscopic bodies, as well as to a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and black hole entropy emerges as entanglement entropy with hidden degrees of freedom. The emergent picture gives a substantial agreement with B-H entropy and Hawking temperature.