2017/12/15 by Y. Kurihara, Kurihara, Yoshimasa
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1712.07964
openalex publication_date 2017/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a quantum gravity equation owing to the geometrical quantization of general relativity, namely the Schrödinger-Einstein equation. Quantum effects of a Schwarzschild black hole are demonstrated by solving the quantum equation requiring a stationary phase; the consistent result is obtained using the Einstein-Brillouin-Keller (EBK) quantization condition. We solve the Schrödinger--Einstein equation around the classical solution of the McVittie-Thakurta metric. This solution simultaneously describes a system with Schwarzschild's black holes and a scalar field. Moreover, we investigate a possible interplay between quantum black holes and a scalar field. The number density of black holes in the universe is obtained by applying statistical mechanics to a system consisting of black holes and a scalar field. A possible solution to the cosmological constant problem is proposed from a statistical perspective.