## “Exploring Non-Perturbative Corrections in Black Hole Thermodynamics”

arXiv:2403.07972v1 Announce Type: new

Abstract: In this paper, we use the holographic principle to obtain a modified metric of black holes that reproduces the exponentially corrected entropy. The exponential correction of the black hole entropy comes from non-perturbative corrections. It interprets as a quantum effect which affects black hole thermodynamics especially in the infinitesimal scales. Hence, it may affect black hole stability at the final stage. Then, we study modified thermodynamics due to the non-perturbative corrections and calculate thermodynamics quantities of several non-rotating black holes.

**Introduction:**

In this paper, we explore the implications of the holographic principle in obtaining a modified metric of black holes. Our goal is to reproduce the exponentially corrected entropy of black holes and understand the quantum effects that may modulate their thermodynamics, particularly at infinitesimal scales and the final stages of their stability.

## Holographic Principle and Modified Metric

The holographic principle is utilized in this study to derive a modified metric for black holes. By incorporating non-perturbative corrections, we aim to capture the exponential correction of the black hole entropy.

### Exponential Correction of Black Hole Entropy

The exponential correction to black hole entropy is attributed to quantum effects. These effects become significant at infinitesimal scales and potentially influence the stability of black holes in their final stages.

### Modified Thermodynamics and Non-perturbative Corrections

We analyze the modified thermodynamics resulting from the incorporation of non-perturbative corrections. By calculating various thermodynamic quantities for non-rotating black holes, we gain insights into the implications of these corrections on the behavior of black holes.

## Roadmap for the Future

- Further Investigation of Quantum Effects: The study of exponential corrections to black hole entropy can be expanded to investigate other quantum effects that may impact black hole thermodynamics. This can provide a deeper understanding of the underlying physics at infinitesimal scales.
- Experimental Validation: Conducting experiments or observations to test the predictions of the modified metric and examine if the non-perturbative corrections can be detected in real-world black holes. This would help confirm the applicability of the holographic principle and the validity of the proposed modifications.
- Exploration of Rotating Black Holes: Extending the analysis to include rotating black holes can reveal additional insights into the interplay between non-perturbative corrections, thermodynamics, and stability in dynamic systems.
- Developing Quantum Gravitational Models: Incorporating the findings of this study into the development of quantum gravitational models can enhance our understanding of the fundamental nature of spacetime and gravity.

## Challenges and Opportunities

**Challenges:**

- Obtaining precise measurements and observational data for black holes at infinitesimal scales or in their final stages of stability can be extremely challenging due to the limitations of current technology and the inherent complexities of these phenomena.
- Theoretical calculations and modeling of black hole thermodynamics with non-perturbative corrections require sophisticated mathematical techniques and assumptions, which may introduce uncertainties and limitations in the obtained results.
- The incorporation of the holographic principle and non-perturbative corrections into existing physical theories, such as general relativity and quantum mechanics, poses challenges in reconciling and integrating these frameworks.

**Opportunities:**

- The potential discovery and understanding of quantum effects at infinitesimal scales and their impact on black hole thermodynamics could revolutionize our understanding of gravity and spacetime.
- Confirmation of the holographic principle and the modifications derived from this study would provide experimental validation of fundamental theories in theoretical physics.
- The exploration of rotating black holes and the interplay between non-perturbative corrections and dynamics can lead to new insights into the behavior and stability of these astrophysical phenomena.
- The development of quantum gravitational models based on the findings of this study can contribute to bridging the gap between general relativity and quantum mechanics, leading to a more comprehensive theory of gravity.

**Conclusion:**

This study demonstrated the application of the holographic principle in obtaining a modified metric for black holes, incorporating non-perturbative corrections to reproduce the exponentially corrected entropy. The implications of these modifications on black hole thermodynamics, especially at infinitesimal scales and the final stages of stability, were examined. The roadmap for future research includes further investigation of quantum effects, experimental validation, exploration of rotating black holes, and the development of quantum gravitational models. While challenges exist in measurement, theory, and integration of frameworks, opportunities for groundbreaking discoveries and advancements in theoretical physics are on the horizon.