Quantum effects of black holes and cosmological constant problem
arXiv:1712.07964
Abstract
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.
27 pages, 1 figure
References in corpus (16)
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
- The Standard Model Higgs boson as the inflaton
- Inflation scenario via the Standard Model Higgs boson and LHC
- Higgs inflation at the critical point
- McVittie's Legacy: Black Holes in an Expanding Universe
- Lectures on the Cosmological Constant Problem
- How the expansion of the universe determines the causal structure of McVittie spacetimes
- Cosmological black holes and white holes with time-dependent mass
- Supergravity Higgs Inflation and Shift Symmetry in Electroweak Theory
- Realistic fluids as source for dynamically accreting black holes in a cosmological background
- Evolving black holes from conformal transformations of static solutions
- Stochastic Metric Space and Quantum Mechanics
- Characteristic classes in general relativity on a modified Poincare curvature bundle
- Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture
- A quantum mass-spectrum of Kerr black hole: superstrings