Anomaly-free deformations of spherical general relativity coupled to matter

Abstract

A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most general Hamiltonian quadratic in radial derivatives of the variables, we obtain a family of effective modified constraints that satisfy Dirac's deformation algebra, which encodes the covariance of general relativity, and show that (scale-dependent) holonomy corrections can be consistently implemented. In vacuum, the deformed anomaly-free Hamiltonian is explicitly written in terms of three free functions and we obtain a weak observable that can be interpreted as the mass of the model. Finally, as a particular example, we present a specific covariant polymeric model that remains regular for any value of the connection components. Some of its physical implications and the relation with previous studies in the literature are commented.

On the fate of quantum black holes

“…In the second category are works that use coordinates in spherical symmetry where the radial coordinate remains spacelike throughout the entire space-time, making it is possible to treat the interior and exterior of the black hole on an equal footing for quantization [29][30][31][32][33][34][35][36][37]. Building on earlier works [11,38], the improved dynamics scheme was recently applied to vacuum spherically symmetric space-times [39][40][41].…”