by jsendak | Nov 18, 2024 | GR & QC Articles
arXiv:2411.09742v1 Announce Type: new
Abstract: The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits.
Future Roadmap: Challenges and Opportunities
Introduction
The motion of compact binaries and the effects of spin on their dynamics have been the subject of extensive research in gravitational physics. In this article, we examine recent findings that address the challenges of comparing the motion of spinning test particles near Kerr black holes in two different limits: the post-Newtonian (PN) limit and the large mass ratio limit. By deriving closed formulas for gauge-invariant actions and frequencies, the authors provide a new dictionary that allows for interpolation between these two limits. In this roadmap, we outline potential challenges and opportunities in this field for readers to explore.
1. Frame and Gauge Choices
One of the main challenges in comparing the PN and large mass ratio limits is the choice of frame and gauge. Frame and gauge choices can significantly impact the equations of motion and make it difficult to directly compare the two limits. Readers interested in this topic should investigate the various frame and gauge choices used in previous studies and their implications on the dynamics of spinning test particles.
2. Spin Configurations
An important aspect of the motion of spinning test particles is the configuration of their spins. Generic spin configurations further complicate the comparison between the PN and large mass ratio limits. Readers interested in this area of research should explore the effects of different spin configurations on the equations of motion and the challenges they pose in finding a consistent dictionary between the two limits.
3. Hamiltonian Perturbation
The derivation of gauge-invariant actions and frequencies provides a valuable tool for comparing the PN and large mass ratio limits. The perturbative expression of the Hamiltonian in terms of action variables up to 3PN allows for a direct comparison with the 1.5 PN action-angle Hamiltonian. Readers can delve into the details of this perturbation approach and its applicability in matching the actions across both systems.
4. Interpolation and New Dictionary
The derived closed formulas for gauge-invariant actions and frequencies serve as the foundation for establishing a new dictionary for interpolation between the PN and large mass ratio limits. Readers interested in this area should investigate the mathematical techniques used in this interpolation process and the accuracy of the matching between the two systems. Additionally, the potential implications of this new dictionary for future gravitational physics research should be explored.
Conclusion
The study of the motion of spinning test particles near Kerr black holes presents exciting challenges and opportunities in gravitational physics research. By addressing the challenges of frame and gauge choices, spin configurations, and establishing a new dictionary for interpolation, this article opens up avenues for further exploration in this field. Readers are encouraged to delve deeper into these topics, contributing to the ongoing understanding of the dynamics of compact binaries and the effects of spin on their motion.
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by jsendak | Jun 7, 2024 | GR & QC Articles
arXiv:2406.03552v1 Announce Type: new
Abstract: Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by coupling to a real scalar field with a Higgs-type potential. The Proca-Higgs model serves as a UV completion of a complex Proca model with self-interactions. Here, we construct and examine the mathematical and physical properties of rotating configurations. In particular, rotation allows horizon-bearing solutions, including stationary clouds surrounding Kerr black holes and their non-linear continuation into black holes with Proca-Higgs hair.
Future Roadmap: Challenges and Opportunities
1. Further Exploration of Rotating Configurations
The construction and examination of rotating configurations in the Einstein-Proca-Higgs model opens up new avenues for research. Continued exploration of these configurations will allow for a deeper understanding of their mathematical and physical properties.
2. Investigation of Horizon-Bearing Solutions
The presence of horizon-bearing solutions indicates the possibility of stationary clouds surrounding Kerr black holes. Investigating these solutions and studying their behavior will provide valuable insights into the dynamics of black holes and their interaction with matter fields.
3. Non-Linear Continuation into Black Holes with Proca-Higgs Hair
By studying the non-linear continuation of the rotating configurations, it becomes possible to understand the formation and properties of black holes with Proca-Higgs hair. This opens the door to exploring the effects of the Proca vector field and Higgs scalar field on the geometry and dynamics of black holes.
4. Mathematical and Physical Analysis
A comprehensive analysis of the mathematical and physical properties of the rotating configurations and their implications is crucial. This includes investigating their stability, energy-momentum content, and effect on the spacetime geometry. Such analysis will provide a solid foundation for future theoretical and observational studies.
5. Potential Challenges
- Complexity of Numerical Simulations: The construction and examination of rotating configurations in the Einstein-Proca-Higgs model may require complex numerical simulations. Overcoming computational challenges and developing efficient numerical techniques will be crucial.
- Theoretical Framework: Exploring rotating configurations and their implications may require a solid theoretical framework that can handle the intricate interplay between the Einstein field equations, Proca-Higgs model, and rotating solutions.
6. Potential Opportunities
- Advancement in Black Hole Studies: Investigating rotating configurations and their non-linear continuation into black holes with Proca-Higgs hair has the potential to advance our understanding of black holes and their interaction with matter fields.
- Implications for Fundamental Physics: Understanding the properties of rotating configurations in the Einstein-Proca-Higgs model can have broader implications for fundamental physics, such as particle physics and cosmology.
In conclusion, the study of rotating configurations in the Einstein-Proca-Higgs model presents exciting opportunities for further research. By exploring these configurations and their implications, researchers can deepen our understanding of black holes, matter fields, and fundamental physics as a whole. However, it is important to address potential challenges in numerical simulations and theoretical frameworks to fully exploit the opportunities these configurations offer.
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by jsendak | Apr 11, 2024 | GR & QC Articles
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.
Field redefinitions and singularity removal:
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.
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by jsendak | Feb 9, 2024 | GR & QC Articles
Black hole superradiance has proven being very valuable in several realms of gravitational physics, and holds a promising discovery potential. In this paper, we show how it can sheed light on a long standing problem in physics, the quest for magnetic monopoles in the Universe. Placing them in the interior of primordial rotating black holes, which act as natural amplifiers, we show that massive charged bosonic fields in their vicinity exhibit a superradiant instability which surpasses significantly that of neutral Kerr black holes. Strikingly, this is true for black holes containing an order-one number of magnetic monopoles, or merely a single one, and possessing either low, moderate or large values of angular momentum. In particular, the instability is drastically faster than the radiative decay time of charged pions, thus making it physically relevant. Furthermore, our analysis identifies the most unstable modes as a class of monopole spheroidal harmonics, that we dub north and south monopole modes, whose morphology is markedly different from the usual superradiantly unstable modes since they extend along the rotational axis. We conclude by discussing implications of our results for primordial magnetic black holes, and their observational signatures as sources of cosmic rays and high-frequency gravitational waves.
Black hole superradiance has been proven to be valuable in various areas of gravitational physics and offers significant potential for discovery. In this paper, we focus on its application to the long-standing challenge of finding magnetic monopoles in the Universe.
We propose that primordial rotating black holes could serve as natural amplifiers for magnetic monopoles placed within their interiors. This amplification leads to a superradiant instability in the vicinity of these black holes, which is even more pronounced than that observed in neutral Kerr black holes. This instability is relevant for black holes containing just one or a small number of magnetic monopoles, regardless of their level of angular momentum.
An interesting finding is that the superradiant instability occurs at a much faster rate than the radiative decay time of charged pions, making it physically relevant. Additionally, our analysis reveals the existence of a specific class of monopole spheroidal harmonics known as north and south monopole modes. These modes differ from the usual superradiantly unstable modes as they extend along the rotational axis of the black hole.
In conclusion, our research has significant implications for understanding primordial magnetic black holes and their potential role as sources of cosmic rays and high-frequency gravitational waves. By exploring the phenomenon of black hole superradiance and its application to magnetic monopoles, we have opened up new avenues for investigation and future discoveries in gravitational physics.
Roadmap for Readers
- Introduction to black hole superradiance and its relevance in gravitational physics
- Discussion of the long-standing problem of finding magnetic monopoles in the Universe
- Explanation of the proposed use of primordial rotating black holes as amplifiers for magnetic monopoles
- Presentation of the superradiant instability observed in the vicinity of these black holes
- Comparison of the instability in black holes with different numbers of magnetic monopoles and levels of angular momentum
- Analysis of the faster rate of the superradiant instability compared to the decay time of charged pions
- Description of the unique monopole spheroidal harmonics known as north and south monopole modes
- Discussion of the implications for primordial magnetic black holes and their potential observational signatures as sources of cosmic rays and high-frequency gravitational waves
- Summary of the key findings and their significance in advancing our understanding of gravitational physics
Potential Challenges and Opportunities
While our research opens up exciting possibilities for further exploration, there are several challenges that need to be addressed:
- Experimental verification: The proposed phenomenon needs to be empirically tested in order to validate its existence.
- Data collection: Gathering observational data on primordial magnetic black holes and their characteristics poses technological and logistical challenges.
- Theoretical refinement: Further theoretical analysis is required to fully understand the underlying mechanisms and implications of the observed superradiant instability.
- Interdisciplinary collaboration: Collaboration between researchers from diverse fields such as astrophysics, particle physics, and gravitational wave astronomy is crucial for comprehensive investigations.
Despite these challenges, the opportunities presented by this research are immense:
- Potential discovery of magnetic monopoles: This research offers a new avenue for detecting elusive magnetic monopoles in the Universe.
- Advancement of gravitational physics: The study of black hole superradiance and its application to magnetic monopoles can significantly contribute to our understanding of gravitational phenomena.
- Expanded knowledge of primordial black holes: Investigating the role of primordial rotating black holes in amplifying magnetic monopoles can shed light on the formation and evolution of these mysterious objects.
- New observational tools: The identification of primordial magnetic black holes as potential sources of cosmic rays and high-frequency gravitational waves opens up new possibilities for detecting and studying these phenomena.
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by jsendak | Jan 20, 2024 | GR & QC Articles
Adiabatic binary inspiral in the small mass ratio limit treats the small body
as moving along a geodesic of a large Kerr black hole, with the geodesic slowly
evolving due to radiative backreaction. Up to initial conditions, geodesics are
typically parameterized in two ways: using the integrals of motion energy $E$,
axial angular momentum $L_z$, and Carter constant $Q$; or, using orbit geometry
parameters semi-latus rectum $p$, eccentricity $e$, and (cosine of )
inclination $x_I equiv cos I$. The community has long known how to compute
orbit integrals as functions of the orbit geometry parameters, i.e., as
functions expressing $E(p, e, x_I)$, and likewise for $L_z$ and $Q$. Mappings
in the other direction — functions $p(E, L_z, Q)$, and likewise for $e$ and
$x_I$ — have not yet been developed in general. In this note, we develop
generic mappings from ($E$, $L_z$, $Q$) to ($p$, $e$, $x_I$). The mappings are
particularly simple for equatorial orbits ($Q = 0$, $x_I = pm1$), and can be
evaluated efficiently for generic cases. These results make it possible to more
accurately compute adiabatic inspirals by eliminating the need to use a
Jacobian which becomes singular as inspiral approaches the last stable orbit.
Mapping Orbit Integrals to Orbit Geometry Parameters
This article discusses the development of mappings from orbit integrals (energy E, axial angular momentum L_z, Carter constant Q) to orbit geometry parameters (semi-latus rectum p, eccentricity e, and inclination x_I). These mappings are essential for accurately computing adiabatic inspirals where a small body moves along the geodesic of a large Kerr black hole.
Current Understanding
The community has long been able to compute orbit integrals as functions of the orbit geometry parameters. However, the reverse mappings, i.e., functions that express p, e, and x_I in terms of E, L_z, and Q, have not yet been developed in general.
New Developments
In this article, the authors present generic mappings that translate E, L_z, and Q into p, e, and x_I. These mappings are particularly simple for equatorial orbits (Q = 0, x_I = ±1) and can be efficiently evaluated for generic cases.
Potential Opportunities
- Accurate Computation: The developed mappings provide a more accurate method to compute adiabatic inspirals, eliminating the need for a singular Jacobian as the inspiral approaches the last stable orbit.
- Improved Understanding: By bridging the gap between orbit integrals and orbit geometry parameters, researchers can gain a deeper understanding of the dynamics of small bodies moving in the vicinity of Kerr black holes.
Potential Challenges
- Validation: The newly developed mappings need to be validated through further research and comparison with existing methods. This will ensure their reliability and accuracy in various scenarios.
- Complex Scenarios: While the mappings are efficient for generic cases, there may be complex scenarios or extreme conditions where their applicability needs to be further studied.
Roadmap for Readers
- Understand the current state of knowledge regarding the computation of orbit integrals and their dependence on orbit geometry parameters.
- Explore the limitations and challenges faced in the absence of reverse mappings from orbit integrals to orbit geometry parameters.
- Examine the new developments presented in this article, focusing on the generic mappings that allow for accurate computation of adiabatic inspirals.
- Consider the potential opportunities stemming from these developments, such as improved accuracy and a deeper understanding of small body dynamics around Kerr black holes.
- Recognize the potential challenges in validating the mappings and their applicability in complex scenarios.
- Stay updated on further research in this field to gain insights into the refinement and expansion of the developed mappings.
In conclusion, this article presents a significant advancement in understanding adiabatic inspirals by developing mappings from orbit integrals to orbit geometry parameters. While offering opportunities for accurate computation and improved understanding, these mappings need validation and careful consideration of their applicability in various scenarios.
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