“Absence of Closed Causal Geodesics in Kerr-Star Spacetime”

arXiv:2409.09094v1 Announce Type: new
Abstract: The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the Kerr spacetime. Despite the presence of closed timelike curves below the inner horizon, we prove that the timelike geodesics cannot be closed in the Kerr-star spacetime. Since the existence of closed null geodesics was ruled out by the author in Sanzeni [arXiv:2308.09631v3 (2024)], this result shows the absence of closed causal geodesics in the Kerr-star spacetime.

The Future of Causal Geodesics in the Kerr-star Spacetime

In a recent study, researchers have examined the properties of the Kerr-star spacetime, an extension of the well-known Kerr spacetime. The Kerr-star spacetime includes regions beyond the horizons and in the negative radial region.

Exploring Timelike Geodesics

One intriguing aspect of the Kerr-star spacetime is the presence of closed timelike curves below the inner horizon. These closed timelike curves have been a subject of interest due to their potential for time travel. However, the researchers have made a fascinating discovery – they have proven that timelike geodesics cannot be closed in the Kerr-star spacetime.

Absence of Closed Causal Geodesics

Moreover, a previous study by author Sanzeni has already ruled out the existence of closed null geodesics in the Kerr-star spacetime. This recent result complements the previous findings by demonstrating the absence of closed causal geodesics as well.

Roadmap for the Future

While the current research sheds light on the topology of the Kerr-star spacetime, there are several avenues for further exploration and challenges to overcome:

1. Understanding the nature of closed timelike curves: Despite the inability to form closed timelike geodesics in the Kerr-star spacetime, the presence of closed timelike curves below the inner horizon remains intriguing. Future studies should delve deeper into the properties and implications of these curves.
2. Extending the analysis to other spacetimes: The results obtained in this study are specific to the Kerr-star spacetime. It would be beneficial to investigate the presence or absence of closed causal geodesics in other spacetimes as well.
3. Examining the consequences of these findings: The absence of closed causal geodesics in the Kerr-star spacetime has implications for our understanding of the behavior of particles and light in this exotic region. Further research should focus on unraveling the consequences of this absence and its potential impact on theoretical models.
4. Experimental validation: While theoretical studies offer deep insights, experimental validation is crucial to confirm the findings. Scientists could design experimental setups or observations to test the predictions and conclusions derived from the Kerr-star spacetime.

Conclusion

The recent research on the Kerr-star spacetime has unveiled the absence of closed causal geodesics, complementing the earlier findings that ruled out closed null geodesics. This opens up new avenues of research into the nature of closed timelike curves, the exploration of other spacetimes, understanding the consequences of these findings, and experimental validation. By delving into these areas, scientists can continue to push the boundaries of our understanding of the Kerr-star spacetime and its implications in the broader context of general relativity and theoretical physics.

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