The enumeration of black hole entropy in candidate theories of quantum gravity utilizes the quantum properties of microstates residing on the black hole horizon. For example, in loop quantum gravity, the computation of entropy is based on the spectrum of the area operator, and one determines the possible number of area microstates corresponding to a given classical horizon area. In this paper, we derive the eigenspectrum of the horizon area operator for rotating/nonrotating black holes in a gravitational theory nonminimally coupled to scalar fields. Using the weak isolated horizon formalism, we show that the spectrum of the area operator follows unambiguously from the algebra of horizon symmetry. More precisely, from the quantum mechanical point of view, the horizon geometry must be naturally discrete, a conclusion that is arrived at directly, without the need for any particular theory of quantum gravity. The area spectrum depends on the Barbero-Immirzi parameter as well as the value of the scalar field on the horizon. The area spectrum is equidistant, which is consistent with the Bekenstein-Mukhanov proposal and gives rise to black hole entropy and their quantum corrections.

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• Alternative gravity theories
• Quantum gravity