  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
$\kappa$-Poincar\'e 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.
