Modified constraint algebra in loop quantum gravity and spacetime interpretation

TL;DR

This paper investigates how inverse triad corrections in loop quantum gravity modify the constraint algebra and explores the implications for spacetime interpretation and black hole horizons, challenging classical notions.

Contribution

It demonstrates that a modified constraint algebra in LQG does not correspond to spacetime coordinate transformations, prompting a reevaluation of black hole horizon definitions.

Findings

Modified constraint algebra does not equate to spacetime covariance.

A revised horizon condition can yield consistent black hole descriptions.

Classical results like mass thresholds and Hawking temperature are slightly altered.

Abstract

Classically the constraint algebra of general relativity, which generates gauge transformations, is equivalent to spacetime covariance. In LQG, inverse triad corrections lead to an effective Hamiltonian constraint which can lead to a modified constraint algebra. We show, using example of spherically symmetric spacetimes, that a modified constraint algebra does not correspond to spacetime coordinate transformation. In such a scenario the notion of black hole horizon, which is based on spacetime notions, also needs to be reconsidered. A possible modification to the classical trapping horizon condition leading to consistent results is suggested. In the case where the constraint algebra is not modified a spacetime picture is valid and one finds mass threshold for black holes and small corrections to Hawking temperature.