“Unified Master Equation for Perturbations around Charged Black Holes”
arXiv:2404.06544v1 Announce Type: new
Abstract: It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner–Nordstr”om black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.
Future Roadmap: Challenges and Opportunities
Introduction
Black holes are fascinating objects in general relativity that have been extensively studied. Previous research has shown that Schwarzschild and Kerr black holes have vanishing tidal Love numbers, a property attributed to the hidden structure of ladder symmetries for perturbations. This article extends the concept of ladder symmetries to non-rotating charged black holes in general relativity. By adopting a more comprehensive definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations, we explore new possibilities and face certain challenges.
Challenges
- An ambiguity in the split between source and response:
Calculating a subset of the couplings in full general relativity poses a challenge due to the ambiguity in the split between source and response. However, this challenge is resolved through an analytic continuation. The resolution of this ambiguity allows us to move forward in our calculations and analysis.
To make the presence of ladder symmetries more evident and remove some of the singularities in previous formulations, nontrivial field redefinitions are required. This process may introduce complexities in the analysis but presents an opportunity to enhance our understanding and develop a more unified approach to perturbations around Reissner-Nordström black holes.
Opportunities
- Deriving a novel master equation:
By resolving the challenges mentioned above and incorporating the ladder symmetries, we are able to derive a novel master equation. This equation unifies scalar, electromagnetic, and gravitational perturbations around Reissner-Nordström black holes. This achievement opens up an opportunity to explore connections between different types of perturbations and deepen our understanding of black hole dynamics.
Conclusion
By adopting a more general definition of Love numbers and extending the ladder symmetries to non-rotating charged black holes in general relativity, this work has achieved significant progress. Overcoming challenges related to the ambiguity in the split between source and response and performing nontrivial field redefinitions, the study has derived a novel master equation that unifies different types of perturbations. This achievement not only allows for better understanding of black hole dynamics but also opens up new opportunities for future research in this field.