Noncommutative Quantum Gravity and Symmetry of Klein-Gordon Equation

Abstract

In the paper 'A New Approach to Quantum Gravity'[1], we suggest a new approach to quantum gravity. Using this theory, we can study the noncommutative gravitational field in momentum space. In this paper, we obtain the general form of the Klein-Gordon equation in noncommutative gravitational field. Then we find the symmetry associated with noncommutative gravity from the Klein-Gordon equation. We study black hole in momentum space and conclude that the event horizon of black holes is formed by the dipoles in momentum space with limit state.