Quantum effects of black holes and cosmological constant problem

TL;DR

This paper introduces a quantum gravity equation called the Schrödinger-Einstein equation, explores quantum effects of black holes, and proposes a statistical approach to address the cosmological constant problem.

Contribution

It formulates a quantum gravity framework and applies it to black holes and scalar fields, offering a novel statistical perspective on the cosmological constant problem.

Findings

Quantum effects of black holes demonstrated using the Schrödinger-Einstein equation.

A statistical model for black hole density in the universe is developed.

A potential solution to the cosmological constant problem is proposed.

Abstract

We propose a quantum gravity equation owing to the geometrical quantization of general relativity, namely the Schr\"{o}dinger-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 Schr\"{o}dinger--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.