# Quantum Effects in General Relativity: Investigating Repulsive Gravity of Black Holes at Large Distances

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## Abstract

**:**

## 1. Introduction

## 2. Cosmological Scalar Boson Mass under Self-Gravity

#### 2.1. Stationary Scalar Mass Distribution

#### 2.2. The Mass Distribution in a Central Symmetric Scalar Uncharged Black Hole

#### 2.3. The Mass Distribution near the Center of a Schwarzschild Black Hole

## 3. Gravitational Field of Black Holes at Large Distance in Spacetime with Background Fluctuations

#### 3.1. Quantum Potential Fluctuations Generated by Background Fluctuations

#### 3.2. Spectrum and Correlation Function of Mass Density Noise in Quantum Spacetime with Curvature Fluctuations

#### 3.3. The (Dark) Energy Density of Quantum Potential Fluctuations

#### 3.4. Repulsive Gravity at Large Distance

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## Appendix B

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Chiarelli, P.
Quantum Effects in General Relativity: Investigating Repulsive Gravity of Black Holes at Large Distances. *Technologies* **2023**, *11*, 98.
https://doi.org/10.3390/technologies11040098

**AMA Style**

Chiarelli P.
Quantum Effects in General Relativity: Investigating Repulsive Gravity of Black Holes at Large Distances. *Technologies*. 2023; 11(4):98.
https://doi.org/10.3390/technologies11040098

**Chicago/Turabian Style**

Chiarelli, Piero.
2023. "Quantum Effects in General Relativity: Investigating Repulsive Gravity of Black Holes at Large Distances" *Technologies* 11, no. 4: 98.
https://doi.org/10.3390/technologies11040098