Rainbow-Like Black-Hole Metric from Loop Quantum Gravity

Hypersurface deformation algebra consists of a fruitful approach to derive deformedsolutions 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 programby k-Poincaré symmetry. Based on this approach, we analyzed the solution derived for theinterior of a black hole and we found similarities with the so-called rainbow metrics, like amomentum-dependence of the metric functions. Moreover, we derived an effective, time-dependentPlanck length and compared different regularization schemes.