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We obtain a novel exact analytical solution to Einstein-Maxwell-scalargravity with negative cosmological constant in (2+1)-dimensions. The scalarfield is minimally coupled to gravity and electromagnetism by the metricansatz. On the one hand, we first find analytical results for the real part ofquasinormal mode spectrum of a rotating hairy Ba\~{n}ados-Teitelboim-Zanelli(BTZ) black hole by solving the associated Dirac equation through thepseudo-Hermitian quantum mechanical tools within the framework ofdiscrete-basis-set method. We then show that, in the spinless case, thesequasinormal modes (QNMs) have equally spaced with respect to the relatedazimuthal quantum number, while the spinning BTZ black hole with scalar hairhas Dirac-like unequally spaced discrete one. Moreover, the analytical resultsfor these QNMs found here are in excellent agreement with those found in theliterature for hairless BTZ black holes. On the other hand, we also develop ananalogue model for this hairy Banados-Teitelboim-Zanelli black hole ingraphene, by mapping it onto the hyperbolic pseudosphere surface with negativecurvature. The model not only offers to make some predictions for thegravity-like phenomena in a curved graphene sheet but also paves the way forreproducing black hole thermodynamics scenarios in two-dimensional topologicalinsulators.

Hairy BTZ black hole and its analogue model in graphene