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Article Dans Une Revue JCAP Année : 2018

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

Jibril Ben Achour
Hongguang Liu
  • Fonction : Auteur
Karim Noui

Résumé

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 -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.

Dates et versions

hal-01815228 , version 1 (13-06-2018)

Identifiants

Citer

Jibril Ben Achour, Frederic Lamy, Hongguang Liu, Karim Noui. Non-singular black holes and the Limiting Curvature Mechanism: A Hamiltonian perspective. JCAP, 2018, 05, pp.072. ⟨10.1088/1475-7516/2018/05/072⟩. ⟨hal-01815228⟩
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