“Singularities in Schwarzschild Geometry Resolved in 2D Dilaton Gravity”

arXiv:2411.10523v1 Announce Type: new
Abstract: We analyze the semiclassical Schwarzschild geometry in the Boulware quantum state in the framework of two-dimensional (2D) dilaton gravity. The classical model is defined by the spherical reduction of Einstein’s gravity sourced with conformal scalar fields. The expectation value of the stress-energy tensor in the Boulware state is singular at the classical horizon of the Schwarzschild spacetime, but when backreaction effects are considered, previous results have shown that the 2D geometry is horizonless and described by a non-symmetric wormhole with a curvature singularity on the other side of the throat. In this work we show that reversing the sign of the central charge of the conformal matter removes the curvature singularity of the 2D backreacted geometry, which happens to be horizonless and asymptotically flat. This result is consistent with a similar analysis recently performed for the CGHS model. We also argue the physical significance of negative central charges in conformal anomalies from a four-dimensional perspective.

Future Roadmap: Challenges and Opportunities

Introduction

In this article, we examine the conclusions drawn from analyzing the semiclassical Schwarzschild geometry in the Boulware quantum state within the framework of two-dimensional (2D) dilaton gravity. The classical model is defined by the spherical reduction of Einstein’s gravity sourced with conformal scalar fields. The expectation value of the stress-energy tensor in the Boulware state is found to be singular at the classical horizon of the Schwarzschild spacetime. However, considering the backreaction effects, previous studies have shown that the 2D geometry becomes horizonless, transforming into a non-symmetric wormhole with a curvature singularity on the other side of the throat. This work presents a new insight into this phenomenon by demonstrating that reversing the sign of the central charge of the conformal matter eliminates the curvature singularity and results in a horizonless and asymptotically flat 2D backreacted geometry. This finding aligns with a similar analysis performed for the CGHS model.

Roadmap

1. Understanding the Boulware Quantum State

Readers should start by familiarizing themselves with the concept of the Boulware quantum state and its implications in the semiclassical Schwarzschild geometry. This state exhibits a singularity at the classical horizon, requiring further investigation to explore its behavior under backreaction effects.

2. Exploring Backreaction Effects

Next, readers should delve into the examination of backreaction effects on the 2D dilaton gravity model. Analyze the previous results that demonstrate the transformation of the horizon into a wormhole with a curvature singularity on the other side of the throat. This offers a unique perspective on the nature of the backreacted geometry.

3. Significance of Negative Central Charges

Consider the implications of reversing the sign of the central charge of the conformal matter. This key finding removes the curvature singularity and results in a horizonless and asymptotically flat 2D backreacted geometry. Relate this result to the recent analysis conducted for the CGHS model, which provides further support for the consistency and significance of negative central charges in conformal anomalies.

4. Physical Significance from a Four-Dimensional Perspective

Finally, readers should evaluate the physical significance of negative central charges in conformal anomalies from a four-dimensional perspective. Reflect on the implications and potential applications of this understanding beyond the 2D dilaton gravity framework.

Challenges and Opportunities

• Challenges:
• Further research is needed to explore the broader implications of the newfound understanding of the curvature singularity and horizonless nature of the 2D backreacted geometry.
• Investigating the compatibility of these findings with other quantum gravity models and theories.
• Addressing potential limitations and assumptions of the 2D dilaton gravity framework and exploring its validity in higher dimensions.
• Opportunities:
• Probing the connection between the reversal of the central charge sign and the elimination of curvature singularities, potentially leading to new insights into the nature of wormholes.
• Exploring the implications of this research in other fields, such as black hole physics, quantum field theory, and quantum gravity.
• Investigating the potential applications in areas like information theory, holography, and cosmology.

Conclusion

This roadmap provides readers with an outline of the future research directions and potential challenges and opportunities in understanding the semiclassical Schwarzschild geometry within the framework of 2D dilaton gravity. By considering the backreaction effects and reversing the sign of the central charge, researchers have discovered a horizonless and asymptotically flat geometry, removing the curvature singularity. Further investigation is required to fully comprehend the physical significance of these findings and their applicability in other quantum gravity models and theories.

References:

arXiv:2411.10523v1 Announce Type: new

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