Quantum effects of black holes and cosmological constant problem
Abstract
We propose a quantum gravity equation owing to the geometrical quantization of general relativity, namely the SchrödingerEinstein 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 EinsteinBrillouinKeller (EBK) quantization condition. We solve the SchrödingerEinstein equation around the classical solution of the McVittieThakurta 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 arXiv:
 arXiv:1712.07964
 Bibcode:
 2017arXiv171207964K
 Keywords:

 Physics  General Physics
 EPrint:
 27 pages, 1 figure