# The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime

**Authors:** Felix Willenborg, Dennis Philipp, Claus Lämmerzahl  
**arXiv:** [2411.19919](https://arxiv.org/abs/2411.19919)  
**Date:** 2024-11-29  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2411.19919v1/

## Key points

- Taub-NUT spacetime is a solution to Einstein's electrovacuum equation, providing insights into gravitational fields
- Misner strings in the Bonnor interpretation resemble Dirac strings from magnetic monopoles
- Scattering phenomena on Taub-NUT spacetime led to discovery of quantization condition involving electric charge and magnetic moment
- Researchers use linear perturbations within Newman-Penrose formalism for studying scattering behavior
- Focus on solving angular Teukolsky equation and deriving eigenvalues using solutions from confluent Heun equation

## Summary

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The Taub-NUT spacetime is a solution to Einstein's electrovacuum equation that offers unique insights into the nature of gravitational fields. In the Bonnor interpretation, intriguing structures known as Misner strings bear a resemblance to Dirac strings found in the realm of magnetic monopoles. The investigation of scattering phenomena in this context has led to the discovery of a quantization condition involving the product of electric charge and magnetic moment, similar to the famous Dirac condition. To delve deeper into the study of scattering on the Taub-NUT spacetime, researchers have employed linear perturbations within the framework of the Newman-Penrose formalism. By separating these perturbations into angular and radial equations, they have been able to focus on understanding the behavior of waves in this unique gravitational environment. Specifically, attention has been given to solving the angular Teukolsky equation and deriving eigenvalues using solutions from the confluent Heun equation for further analysis. In contrast to some interpretations, such as that by Bonnor, where no direct analog property to the Dirac condition exists in relation to Taub-NUT spacetime parameters remain flexible and unconstrained. However, for specific parameter choices, it is possible to rediscover well-known conditions like the "Misner" condition – where a particular product involving frequency and NUT charge yields an integer value – along with additional considerations incorporating parameters like those introduced by Manko-Ruiz. The outcomes of this research hold promise for analytical investigations into wave-optical scattering phenomena on Taub-NUT black holes. By leveraging these findings, scientists can gain valuable insights into how electromagnetic waves interact with these exotic spacetimes and potentially uncover new perspectives on their wave-optical properties.