Rainbow-Like Black-Hole Metric from Loop Quantum Gravity

Abstract

The hypersurface deformation algebra consists in a fruitful approach to derive deformed solutions of general relativity based on symmetry considerations with quantum gravity effects, whose linearization has been recently demonstrated to be connected to the DSR program by the κ-Poincaré symmetry. Based on this approach, we analyzed the solution derived for the interior of a black hole and we found similarities with the, so called, rainbow metrics, like a momentum-dependence of the metric functions. Moreover, we derived an effective, time-dependent Planck length and compared different regularization schemes.

Mass and horizon Dirac observables in effective models of quantum black-to-white hole transition

“…The application of LQG techniques to other spacetime singularities such as those occurring inside a black hole (BH) is however still limited. Despite of the large effort, no definite consensus has been reached so far and several effective models have been proposed [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The starting point of these models is the observation that the interior region of Schwarzschild black holes, foliated with respect to the radial time-like coordinate, can be modelled as a Kantowski-Sachs cosmological spacetime so that techniques from homogeneous and nonisotropic LQC can be applied to construct the effective quantum theory.…”

Deformed General Relativity and Quantum Black Holes Interior

“…Following this strategy, one found effective geometries where the singular vacuum Schwarzschild interior has been replaced by a black-to-white hole bounce, first in [25,26], and more recently in [27,28]. These new solutions have been discussed in [29][30][31] and an alternative effective polymer model of black-to-white hole transition, providing several improvements, has been introduced in [32][33][34] (see also [35][36][37][38][39][40][41][42][43][44] for additional investigations on polymer black hole geometries and [45][46][47][48] for yet another class of effective models of blackto-white hole transition). While these classical polymer constructions provide a straightforward and interesting platform to investigate quantum corrected effective metrics, the strategy employed in these hamiltonian constructions turns out to suffer from several shortcomings related to the covariance of the quantum corrections.…”

Editorial for the Special Issue “Progress in Group Field Theory and Related Quantum Gravity Formalisms”

“…This can in turn be interpreted as a quantum deformation of general covariance, required by the existence of a new invariant length scale, the Planck scale. In Rainbow-Like Black-Hole Metric from Loop Quantum Gravity [17], Iarley P. Lobo and Michele Ronco investigate spherically-symmetric black hole solutions predicted by effective models of LQG. They show that their quantum-deformed covariance leads to a modified dispersion relation for the total radial momentum, which they then analyse within the paradigm of rainbow gravity.…”