# Rainbow-like Black Hole metric from Loop Quantum Gravity

## TL;DR

This paper derives a rainbow-like black hole metric from Loop Quantum Gravity, revealing momentum-dependent spacetime structures and effective Planck length variations, connecting quantum gravity effects with deformed relativistic symmetries.

## Contribution

It introduces a novel black hole solution exhibiting rainbow metric features derived from Loop Quantum Gravity and analyzes the implications of different regularization schemes.

## Key findings

- Identified momentum-dependent metric functions similar to rainbow metrics.
- Derived an effective, time-dependent Planck length.
- Compared various regularization schemes in the quantum gravity context.

## 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 $\kappa$-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.