# The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method

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## Abstract

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## 1. Introduction

## 2. The Black Hole Solution in Massive Gravity

## 3. The Bogoliubov Transformation Method in Massive Gravity: Hawking Radiation

#### 3.1. The Case of GR: Observers Defining the Time in Agreement with ${T}_{0}(r,t)$ in Massive Gravity

#### 3.2. The Case of Observers Defining the Time Arbitrary

## 4. The Path Integral Formulation of the Black Hole Radiation in Massive Gravity

#### Further Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Penrose diagram for the Schwarzschild geometry in GR as is shown in [5]. In Massive Gravity, the same diagram is valid if we express the black hole solution in terms of the Stückelberg functions. The past-null infinity (${J}^{-}$) of the diagram corresponds to the event where the black hole has not yet formed. The future null infinity (${J}^{+}$), on the other hand, corresponds to the case where the black hole is already formed.

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**MDPI and ACS Style**

Arraut, I.; Segovia, C.; Rosado, W.
The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method. *Universe* **2023**, *9*, 228.
https://doi.org/10.3390/universe9050228

**AMA Style**

Arraut I, Segovia C, Rosado W.
The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method. *Universe*. 2023; 9(5):228.
https://doi.org/10.3390/universe9050228

**Chicago/Turabian Style**

Arraut, Ivan, Carlos Segovia, and Wilson Rosado.
2023. "The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method" *Universe* 9, no. 5: 228.
https://doi.org/10.3390/universe9050228