by jsendak | Sep 5, 2024 | GR & QC Articles
arXiv:2409.02188v1 Announce Type: new
Abstract: Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is the granularity of spacetime, which suggests that free particles would deviate from classical geodesics by following a covariant Brownian motion. This notion is further supported by swerves models in causal set theory, a discrete approach to quantum gravity. At an effective level, such deviations are described by a stochastic correction to the geodesic equation. We show that the form of this correction is strictly restricted by covariance and the mass-shell condition. Under minimal coupling to curvature, the resulting covariant Brownian motion is unique. The process is equivalently described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space. When applied to dark matter particles, covariant Brownian motion results in spontaneous warming at late times, suppressing the matter power spectrum at small scales in a time-dependent manner. Using bounds on the diffusion rate from CMB and growth history measurements of $fsigma_8$, we show that the model offers a resolution to the $S_8$ tension. Future studies on the model’s behavior at non-linear cosmological scales will provide further constraints and, therefore, critical tests for the viability of stochastic dark matter.
Quantum Gravity and Cosmological Models
In order to bridge the gap between theory and observations in quantum gravity, it is important to develop effective cosmological models that take into account the fundamental aspects of quantum gravity. One key aspect to consider is the granularity of spacetime, which suggests that particles may deviate from classical geodesics and instead follow a covariant Brownian motion. This idea is supported by swerves models in causal set theory, a discrete approach to quantum gravity.
The Stochastic Correction and Covariant Brownian Motion
At an effective level, the deviations from classical geodesics are described by a stochastic correction to the geodesic equation. The form of this correction is strictly restricted by covariance and the mass-shell condition. When considering minimal coupling to curvature, it is found that the resulting covariant Brownian motion is unique. This process can also be described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space.
Covariant Brownian Motion and Dark Matter
When applied to dark matter particles, covariant Brownian motion leads to spontaneous warming at late times. This has the effect of suppressing the matter power spectrum at small scales in a time-dependent manner.
Resolution to the S8 Tension
By using bounds on the diffusion rate from measurements of the cosmic microwave background (CMB) and the growth history of the universe ($fsigma_8$), it is shown that the model of covariant Brownian motion offers a resolution to the tension in the determination of the parameter $S_8$.
Future Challenges and Opportunities
Future studies on the behavior of the model at non-linear cosmological scales will provide further constraints and critical tests for the viability of stochastic dark matter. This will be crucial in determining the potential of covariant Brownian motion as a model for quantum gravity and its compatibility with observational data.
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by jsendak | Jul 2, 2024 | GR & QC Articles
arXiv:2407.00174v1 Announce Type: new
Abstract: Gravitational wave memory is said to arise when a gravitational wave burst produces changes in a physical system that persist even after the wave has passed. This paper analyzes gravitational wave bursts in plane wave spacetimes, deriving memory effects on timelike and null geodesics, massless scalar fields, and massless spinning particles whose motion is described by the spin Hall equations. All associated memory effects are found to be characterized by four “memory tensors,” three of which are independent. These tensors form a scattering matrix for the transverse components of geodesics. However, unlike for the “classical” memory effect involving initially comoving pairs of timelike geodesics, one of our results is that memory effects for null geodesics can have strong longitudinal components. When considering massless particles with spin, we solve the spin Hall equations analytically by showing that there exists a conservation law associated with each conformal Killing vector field. These solutions depend only on the same four memory tensors that control geodesic scattering. For massless scalar fields, we show that given any solution in flat spacetime, a weak-field solution in a plane wave spacetime can be generated just by differentiation. Precisely which derivatives are involved depend on the same four memory tensors, and the derivative operators they determine can be viewed as “continuum” memory effects.
Gravitational Wave Memory: Current Analysis and Future Roadmap
Gravitational wave memory, the persistence of changes in a physical system even after a gravitational wave has passed, is the subject of this paper. The analysis focuses on gravitational wave bursts in plane wave spacetimes and explores the memory effects on various entities.
Current Conclusions
The analysis reveals several important findings:
- Memory effects on timelike and null geodesics, as well as massless scalar fields and massless spinning particles, are examined.
- Four independent “memory tensors” are identified, which ultimately form a scattering matrix for the transverse components of geodesics.
- While classical memory effects involve comoving pairs of timelike geodesics, this study shows that memory effects for null geodesics can have strong longitudinal components.
- For massless particles with spin, the study provides analytical solutions to the spin Hall equations, revealing a conservation law associated with each conformal Killing vector field.
- Massless scalar fields in flat spacetime can generate weak-field solutions in plane wave spacetime through differentiation, with the specific derivatives determined by the four memory tensors.
Future Roadmap
Building on these conclusions, the future roadmap for readers includes both challenges and opportunities:
- Further Exploration: Researchers can expand the analysis to investigate additional physical systems and their memory effects under different gravitational wave burst scenarios. This could involve exploring different spacetime geometries and considering the effects on other types of particles or fields.
- Quantifying Memory Effects: Attempts should be made to quantify the memory effects identified in this study. Understanding the magnitudes and durations of these effects will help in predicting and detecting them in real-world scenarios.
- Experimental Validation: Experimental efforts should be directed towards verifying the existence and characteristics of gravitational wave memory effects predicted in this analysis. This could involve designing and conducting experiments using suitable instruments and detectors.
- Applications and Implications: Exploring potential applications and implications of gravitational wave memory effects could lead to the development of new technologies and techniques. For example, memory effects could be leveraged for information storage or novel forms of sensing.
While the road ahead presents challenges in terms of further research and experimental validation, it also offers exciting opportunities for advancing our understanding of gravitational wave memory and harnessing its potential benefits.
Reference: arXiv:2407.00174v1
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by jsendak | Apr 15, 2024 | GR & QC Articles
arXiv:2404.08026v1 Announce Type: new
Abstract: The investigation of non-vacuum cosmological backgrounds containing black holes is greatly enhanced by the Kiselev solution. This solution plays a crucial role in understanding the properties of the background and its relationship with the features of the black hole. Consequently, the gravitational memory effects at large distances from the black hole offer a valuable means of obtaining information about the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole. This paper investigates the gravitational memory effects in the context of the Kiselev solution through two distinct approaches. At first, the gravitational memory effect at null infinity is explored by utilizing the Bondi-Sachs formalism by introducing a gravitational wave (GW) pulse to the solution. The resulting Bondi mass is then analyzed to gain further insight. Therefore, the Kiselev solution is being examined to determine the variations in Bondi mass caused by the pulse of GWs. The study of changes in Bondi mass is motivated by the fact that it is dynamic and time-dependent, and it measures mass on an asymptotically null slice or the densities of energy on celestial spheres. In the second approach, the investigation of displacement and velocity memory effects is undertaken in relation to the deviation of two neighboring geodesics and the deviation of their derivative influenced by surrounding field parameter N and the hair of hairy Kiselev black hole. This analysis is conducted within the context of a gravitational wave pulse present in the background of a hairy Kiselev black hole surrounded by a field parameter N.
Gravitational Memory Effects in the Context of the Kiselev Solution
The Kiselev solution is a valuable tool in understanding non-vacuum cosmological backgrounds that contain black holes. By examining the properties of the background and its relationship with the black hole, we can gain insights into the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole.
Approach 1: Gravitational Memory Effect at Null Infinity
In the first approach, we explore the gravitational memory effect at null infinity using the Bondi-Sachs formalism. To introduce a gravitational wave pulse to the solution, we analyze the resulting Bondi mass. The variations in Bondi mass caused by the pulse of gravitational waves will provide us with valuable insights.
Approach 2: Displacement and Velocity Memory Effects
In the second approach, we investigate the displacement and velocity memory effects in relation to the deviation of two neighboring geodesics and the deviation of their derivative. This analysis takes into account the surrounding field parameter N and the hair of the hairy Kiselev black hole, as well as a gravitational wave pulse present in the background.
Roadmap for Future Research
Understanding the gravitational memory effects in the context of the Kiselev solution opens up several avenues for future research. Here are some potential challenges and opportunities that lie on the horizon:
- Further investigating the relationship between the surrounding field parameter N and the properties of the black hole
- Exploring the impact of different parameters related to the hair of the hairy Kiselev black hole on the gravitational memory effects
- Studying the dynamic and time-dependent nature of the Bondi mass and its implications on mass measurement and energy densities
- Examining the role of the gravitational wave pulse in influencing the displacement and velocity memory effects
By addressing these challenges and pursuing these opportunities, we can deepen our understanding of non-vacuum cosmological backgrounds containing black holes and gain valuable insights into the nature of the Kiselev solution.
Original Article: “Gravitational Memory Effects in the Context of the Kiselev Solution” by [Author Name]
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by jsendak | Mar 19, 2024 | GR & QC Articles
arXiv:2403.10605v1 Announce Type: new
Abstract: We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordstr”om, among others.
Future Roadmap: Challenges and Opportunities on the Horizon
Introduction
In this study, we delve into the fascinating realm of photon rings in a diverse range of axisymmetric black holes. Our primary objective is to examine the physics of these photon rings and explore the potential applications and possibilities they offer. We also discuss the relevance of our findings to various black hole types and their implications in astrophysical scenarios. Below, we outline a future roadmap for readers, highlighting the challenges and opportunities on the horizon.
Understanding the Physics of Photon Rings
To comprehend the physics behind photon rings, we start by investigating black holes that allow for a separable Hamilton-Jacobi equation for the geodesics. Through careful analysis and utilization of the Killing-Yano tensor, we obtain the Penrose limit of these black holes. This important result describes the physics occurring near the photon ring, a crucial region of interest.
Linking the Plane Wave Geometry and Wave Equation
The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation. By studying these connections, we gain insights into the instabilities and Lyapunov exponents of the null geodesics. These Lyapunov exponents and frequencies of photon geodesics, along with the quasinormal modes, can be extracted from the Hamiltonian in the Penrose limit plane wave metric.
Potential Bounds and Inverted Harmonic Oscillators
We further explore the potential bounds on the Lyapunov exponent, the orbital and precession frequencies. We establish connections between these quantities and corresponding inverted harmonic oscillators. This analysis offers intriguing possibilities for understanding the behavior and limitations of photon rings in different black hole spacetimes.
Holographic Duality Framework for Astrophysical Black Holes
Our investigation also delves into the concept of holographic horizons and their applicability to astrophysical black holes. We examine the potential of photon rings serving as holographic horizons within a holographic duality framework. This framework opens up new avenues for understanding the nature of black holes and their connection to holography.
Applicability to Various Black Hole Types
Our formalism is applicable to a wide range of black hole types. We consider stationary black holes like Kerr and Kerr-Newman, as well as static black holes such as Schwarzschild and Reissner-Nordström, among others. This broad applicability enhances the relevance and potential impact of our findings in diverse astrophysical scenarios.
Conclusion
By delving into the physics of photon rings in a range of axisymmetric black holes, we have uncovered valuable insights and potential applications. Our investigation into the Penrose limit, the relationship to frequency matrices and Lyapunov exponents, as well as the exploration of holographic horizons, sets the stage for exciting future research. Despite potential challenges in terms of computational complexity and theoretical formulation, the opportunities for advancing our understanding of black holes and their dynamics are vast.
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by jsendak | Feb 17, 2024 | GR & QC Articles
arXiv:2402.09435v1 Announce Type: new
Abstract: Black bounces are spacetimes that can be interpreted as either black holes or wormholes depending on specific parameters. In this study, we examine the Simpson-Visser and Bardeen-type solutions as black bounces and investigate the gravitational wave in the background of these solutions. We then explore the displacement and velocity memory effects by analyzing the deviation of two neighboring geodesics and their derivatives influenced by the magnetic charge parameter a. This investigation aims to trace the magnetic charge in the gravitational memory effect. Additionally, we consider another family of traversable wormhole solutions obtained from non-exotic matter sources to trace the electric charge Qe in the gravitational memory effect, which can be determined from the far field asymptotic. This project is significant not only for detecting the presence of compact objects like wormholes through gravitational memory effects but also for observing the charge Qe, which provides a concrete realization of Wheeler’s concept of “electric charge without charge.”
Investigating Black Bounces and Gravitational Waves
In this study, we delve into the fascinating concept of black bounces – spacetimes that can be interpreted as both black holes and wormholes depending on certain parameters. Specifically, we examine two types of solutions known as the Simpson-Visser and Bardeen-type solutions, treating them as black bounces. Our goal is to understand the behavior of gravitational waves in the background of these solutions.
Analyzing Displacement and Velocity Memory Effects
To gain deeper insights, we focus on the displacement and velocity memory effects by studying the deviation between two neighboring geodesics and their derivatives, which are influenced by the magnetic charge parameter known as a. By tracing the magnetic charge, we aim to uncover its role in the gravitational memory effect.
Non-Exotic Traversable Wormholes and Electric Charge
In addition to investigating black bounces, we also explore another family of traversable wormhole solutions obtained from non-exotic matter sources. Here, our aim is to trace the electric charge Qe in the gravitational memory effect, which can be determined from the far field asymptotic.
Future Roadmap: Challenges and Opportunities
- Challenges: The investigation of black bounces and their gravitational wave behavior presents some challenges. Understanding the complex dynamics of spacetime, particularly when it can be interpreted as both a black hole and a wormhole, requires advanced mathematical techniques and in-depth analysis.
- Opportunities: Despite the challenges, our research offers exciting opportunities. By studying displacement and velocity memory effects, we may gain valuable insights into the characteristics and nature of black bounces. Additionally, tracing the magnetic charge and electric charge in the gravitational memory effect can potentially lead to the detection and observation of compact objects like wormholes and Wheeler’s concept of “electric charge without charge.”
Conclusion
This project holds significant scientific importance. Through our investigation of black bounces, gravitational waves, and memory effects, we aim to contribute to our understanding of the fundamental nature of spacetime. Furthermore, the potential detection of wormholes and observation of electric charge without charge would mark major milestones in astrophysics and shape our understanding of the universe.
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