# Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. UV-Finiteness

#### 1.2. Asymptotic Safety

#### AS for Dimensionless Couplings and Dimensional Transmutation for Dimensionful Ones

## 2. Six-Derivative Gravitational Model

#### 2.1. Killer Terms

## 3. UV-Finiteness versus Asymptotic Safety in Six-Derivative Gravitational Model

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Note

1 | Another options for a consistent resolution of GR spacetime singularities are provided by some non-local models or when one adds ${\mathcal{R}}^{3}$ operators (and higher) since they are sufficient to solve black hole singularities problem even in the presence of the Einstein–Hilbert part of the action (see, e.g., [79,80]). |

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Rachwał, L.
Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories. *Universe* **2022**, *8*, 229.
https://doi.org/10.3390/universe8040229

**AMA Style**

Rachwał L.
Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories. *Universe*. 2022; 8(4):229.
https://doi.org/10.3390/universe8040229

**Chicago/Turabian Style**

Rachwał, Lesław.
2022. "Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories" *Universe* 8, no. 4: 229.
https://doi.org/10.3390/universe8040229