Inhomogeneities, loop quantum gravity corrections, constraint algebra and general covariance

Understand

Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra.

• Such a deformation implies that the effective theory is no longer generally covariant.
• As a consequence, the geometrical concepts used in the classical theory lose their meaning.
• In the present paper we propose a method, based on canonical transformation on the phase space of the spherically symmetric effective theory, to systematically recover the classical constraint algebra in the presence of the inverse triad corrections as well as in the presence of the holonomy corrections.