Black Holes, Gravitational Waves and Quantum Gravity

Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric quantities such as area and volume are quantized in terms of the Planck length. In this paper we present the basic ideas for a future, mathematically more rigorous, attempt to combine black holes and gravitational waves using the quantization of geometric quantities introduced by Loop Quantum Gravity.