# The quantum gravity of a gravitational wave from a black hole

Comments: 18 pages, 12 figures

In this paper, we investigate the quantum gravity of a gravitational wave emitted by a black hole. We apply the noncommutative Kondo-Takahashi-Zanjic (KTZ) formalism to the Hamiltonian of the Higgs mechanism. In this framework, we construct a one-parameter family of $Q$-invariant quantum field theories and show that they are generalizations of the generalized Einstein-Hilbert action. Using this property, we relate the quantum gravity of the Higgs mechanism to the quantum gravity of the quantum gravity. A simple solution is given to the Schr\"odinger equation in the low-energy limit.