## Title: Resolving Schwarzschild Singularity with Higher-Curvature Corrections: A Roadmap for

arXiv:2403.04827v1 Announce Type: new

Abstract: We show via an explicit construction how an infinite tower of higher-curvature corrections generically leads to a resolution of the Schwarzschild singularity in any spacetime dimension $D ge 5$. The theories we consider have two key properties that ensure the results are general and robust: (1) they provide a basis for (vacuum) gravitational effective field theory in five and higher-dimensions, (2) for each value of the mass, they have a unique static spherically symmetric solution. We present several exact solutions of the theories that include the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones. Unlike previous constructions, these regular black holes arise as vacuum solutions, as we include no matter fields whatsoever in our analysis. We show how the black hole thermodynamics can be studied in a completely universal and unambiguous way for all solutions.

In this article, the authors discuss their findings on how an infinite tower of higher-curvature corrections can resolve the Schwarzschild singularity in spacetime dimensions greater than or equal to five. They highlight two key properties of the theories they consider: (1) they provide a basis for gravitational effective field theory in higher dimensions and (2) they have unique static spherically symmetric solutions for each mass value. Several exact solutions, including the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones, are presented. Notably, these regular black holes are vacuum solutions, meaning no matter fields are included in the analysis. Furthermore, the authors demonstrate that the black hole thermodynamics can be universally and unambiguously studied for all solutions.

## Future Roadmap

Moving forward, this research opens up exciting possibilities and avenues for exploration. Here is a potential roadmap for readers interested in this topic:

### 1. Further Analysis of Higher-Curvature Corrections

To deepen our understanding of the resolution of the Schwarzschild singularity, future research should focus on a more detailed analysis of the infinite tower of higher-curvature corrections. By examining the effects of these corrections on the black hole solutions, researchers can gain insights into the underlying physics and test the robustness of the findings.

### 2. Exploration of Alternative Vacuum Solutions

While the article presents several exact solutions, such as the Hayward black hole and metrics similar to the Bardeen and Dymnikova ones, there may be additional vacuum solutions yet to be discovered. Researchers can investigate alternative mathematical formulations, explore different boundary conditions, or consider variations in the theories to uncover new regular black holes that arise without matter fields.

### 3. Thermodynamics of Regular Black Holes

The article briefly mentions the study of black hole thermodynamics in a universal and unambiguous way for all solutions. Future studies can delve deeper into this aspect, examining the thermodynamic properties, entropy, and behavior of regular black holes. Understanding the thermodynamics of these black holes can provide valuable insights into their stability, relation to information theory, and potential connections with other areas of physics.

### 4. Experimental and Observational Verifications

While the theoretical findings are intriguing, it is essential to test them against observational and experimental data. Researchers can explore the possibility of detecting regular black holes or their effects in astrophysical observations, gravitational wave detections, or particle accelerator experiments. Such verifications would provide strong evidence for the existence and significance of these regular black holes.

### 5. Application to Cosmological Models

Considering the implications of regular black holes for cosmology is another exciting avenue to explore. Researchers can investigate how these black holes might affect the evolution of the universe, the nature of the early universe, or the behavior of dark matter and dark energy. By incorporating the findings into cosmological models, we can gain a more comprehensive understanding of the universe’s dynamics and address open questions in cosmology.

## Challenges and Opportunities

While the research presents exciting possibilities, it also comes with its set of challenges and opportunities:

**Theoretical Challenges:**Exploring the infinite tower of higher-curvature corrections and their effects on gravitational theories is a complex task. Researchers will need to develop advanced mathematical techniques, computational tools, and frameworks to simplify and analyze these theories effectively.**Experimental Limitations:**Verifying the existence of regular black holes or their effects experimentally can be challenging. Researchers may face limitations in observational data, the sensitivity of detectors, or the feasibility of conducting certain experiments. Developing innovative detection methods or collaborations between theorists and experimentalists could help overcome these limitations.**Interdisciplinary Collaboration:**Given the wide-ranging implications of this research, interdisciplinary collaboration between theorists, astrophysicists, cosmologists, and experimentalists is essential. Leveraging expertise from different fields can help address challenges, provide diverse perspectives, and stimulate further breakthroughs.**Public Engagement:**Communicating the significance of regular black holes to the general public and garnering support for future research may require effective science communication strategies. Researchers can engage with the public through popular science articles, public talks, or interactive exhibitions to foster interest and increase awareness.

Overall, the resolution of the Schwarzschild singularity through an infinite tower of higher-curvature corrections holds great potential for advancing our understanding of gravity, black holes, and the universe. By following the outlined roadmap, overcoming challenges, and seizing opportunities, researchers can continue to explore and uncover the fascinating properties and implications of regular black holes.