*Article* **Rainbow-Like Black-Hole Metric from Loop Quantum Gravity**

### **Iarley P. Lobo 1,\* and Michele Ronco 2**


Received: 18 October 2018; Accepted: 28 November 2018; Published: 1 December 2018

**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.

**Keywords:** quantum-gravity phenomenology; hypersurface deformation algebra; loop quantum gravity; black holes
