Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective

TL;DR

This paper analyzes non-singular black holes in mimetic gravity with limiting curvature from a Hamiltonian perspective, exploring their relation to loop quantum gravity and proposing a covariant effective theory with holonomy-like corrections.

Contribution

It introduces a Hamiltonian formulation of non-singular black holes in mimetic gravity, compares them with loop quantum gravity models, and constructs a covariant effective theory with metric-dependent corrections.

Findings

Black holes have no singularity due to limiting curvature.

Mimetic gravity with limiting curvature does not fully reproduce loop quantum gravity dynamics.

A covariant effective theory with holonomy-like corrections is proposed.

Abstract

We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the $\bar{\mu}$-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.