Rainbow-like black-hole metric from loop quantum gravity

Abstract

Hypersurface deformation algebra consists of a fruitful approach to derive deformed solutions of general relativity based on symmetry considerations with quantum-gravity effects, of which the linearization has been recently demonstrated to be connected to the DSR program by 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.