Spectral geometry and black holes degrees of freedom

In this work we show that the introduction of an appropriate cutoff in the spectra of the Laplacian of an spherically symmetric and static black hole reveals an equivalence between shape and holographic degrees of freedom. Even more, the aforementioned cutoff introduces a correction to the Bekenstein-Hawking entropy which resembles the corresponding holographic loop quantum gravity, generalized uncertainty principle and entanglement entropy corrections. The difficulty of extending our results to nonspherically symmetric black holes is pointed out.