Classical Gravitational Waves Research Articles

Next-to-eikonal corrected double graviton dressing and gravitational wave observables at OG2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}^2\\right) $$\\end{document}

Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived from a generalized Wilson line operator in the worldline formalism by integrating over fluctuations of the eikonal trajectories of external particles in gravitationally interacting theories. The dressing can be expressed as a product of exponential terms — a coherent piece with contributions to all odd orders in the gravitational coupling constant and a term quadratic in graviton modes, with the former providing classical gravitational wave observables. In particular, the coherent dressing involves Oκ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\kappa}^3\\right) $$\\end{document} subleading double graviton corrections to the Weinberg soft factor. We use this dressing to derive expressions for the waveform, radiative momentum spectrum and angular momentum. In a limiting case of the waveform, we derive the nonlinear memory effect resulting from the emission of nearly soft gravitons from a scattering process.

Quantum ballet by gravitational waves: Generating entanglement's dance of revival-collapse and memory within the quantum system

Recent proposals are emerging for the experimental detection of entanglement mediated by classical gravity, carrying significant theoretical and observational implications. In fact, the detection of gravitational waves (GWs) in LIGO provides an alternative laboratory for testing various gravity-related properties. By employing LIGO's arms as oscillators interacting with gravitational waves (GWs), our study demonstrates the potential for generating quantum entanglement between two mutually orthogonal modes of simple harmonic oscillators. Our findings reveal unique entanglement dynamics, including periodic “collapse and revival” influenced by GW oscillations, alongside a distinct “quantum memory effect.” Effectively, each harmonic oscillator feels a temperature. We believe that these forecasts may hold significance towards both theoretically probing and experimentally verifying various properties of classical gravitational waves.

Graviton detection and the quantization of gravity

We revisit a question asked by Dyson: “Is a graviton detectable?” We demonstrate that in both Dyson’s original sense and in a more modern measurement-theoretic sense, it is possible to construct a detector sensitive to single gravitons, and in fact a variety of existing and near-term gravitational wave detectors can achieve this. However, while such a signal would be consistent with the quantization of the gravitational field, we draw on results from quantum optics to show how the same signal could just as well be explained via classical gravitational waves. We outline the kind of measurements that would be needed to demonstrate quantization of gravitational radiation and explain why these are substantially more difficult than simply counting graviton clicks or observing gravitational noise in an interferometer, and likely impossible to perform in practice. Published by the American Physical Society 2024

The quantum optics of gravitational waves

By utilizing quantum optics techniques, we examine the characteristics of a quantum gravitational wave (GW) signature at interferometers. In particular, we study the problem by analyzing the equations of motion of a GW interacting with an idealized interferometer. Using this method, we reconstruct the classical GW signal from a representation of the quantum version of an almost classical monochromatic wave (a single-mode coherent state), then we discuss the experimental signatures of some specific, more general quantum states. We calculate the observables that could be used at future interferometers to probe possible quantum states carried by the GWs.

Bound on quantum fluctuations in gravitational waves from LIGO-Virgo

We derive some of the central equations governing quantum fluctuations in gravitational waves, making use of general relativity as a sensible effective quantum theory at large distances. We begin with a review of classical gravitational waves in general relativity, including the energy in each mode. We then form the quantum ground state and coherent state, before then obtaining an explicit class of squeezed states. Since existing gravitational wave detections arise from merging black holes, and since the quantum nature of black holes remains puzzling, one can be open-minded to the possibility that the wave is in an interesting quantum mechanical state, such as a highly squeezed state. We compute the time and space two-point correlation functions for the quantized metric perturbations. We then constrain its amplitude with LIGO-Virgo observations. Using existing LIGO-Virgo data, we place a bound on the (exponential) squeezing parameter of the quantum gravitational wave state of ζ < 41.

Gravitational wave matched filtering by quantum Monte Carlo integration and quantum amplitude amplification

The speedup of heavy numerical tasks by quantum computing is now actively investigated in various fields including data analysis in physics and astronomy. In this paper, we propose a quantum algorithm for matched filtering in gravitational wave (GW) data analysis based on the previous work by Gao et al. [Phys. Rev. Research 4, 023006 (2022)]. Our approach uses the quantum algorithm for Monte Carlo integration for the signal-to-noise ratio (SNR) calculation instead of the fast Fourier transform used in Gao et al. and searches signal templates with high SNR by quantum amplitude amplification. In this way, we achieve an exponential reduction of the qubit number compared with Gao et al.'s algorithm, keeping a quadratic speedup over classical GW matched filtering with respect to the template number.

Why Newtonian gravity is an electromagnetic wave

In this brief communication, we have hypothesized that since Newtonian gravity intimately interacts with classical gravitational waves, it must also be perceivable and mathematically expressible as a wave. It has been shown that Newtonian gravity can be represented as an electromagnetic wave of a particular wavelength &lt;mml:math display="inline"&gt; &lt;mml:mi&gt;λ&lt;/mml:mi&gt; &lt;/mml:math&gt; , propagating at the speed of light, c and with a radius of &lt;mml:math display="inline"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;z&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;λ&lt;/mml:mi&gt; &lt;mml:mo&gt;/&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;π&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; . The waves period is given by T = c/g, and thus acceleration due to gravity is representable as g = cf, where f is position dependent, and thus unique for all orbiting planetary bodies. On the Earth surface, this value is ≅32.71 nHz.

Echoes from quantum black holes

One of the most triumphant predictions of the theory of general relativity was the recent LIGO-Virgo detection of gravitational-wave (GW) signals produced in binary black hole (BH) mergers. However, it is suggested that exotic compact objects, proposed in quantum gravity models of BHs, may produce similar classical GW waveforms, followed by delayed repeating ``echoes.'' In a companion paper [1], we have presented different arguments for a universal Boltzmann reflectivity of quantum BH horizons. Here, we investigate the resulting echoes from this prescription. We derive corresponding quasinormal modes (QNMs) for quantum BHs analytically, and show how their initial conditions can be related to the QNMs of classical BHs. Ergoregion instability is suppressed by the imperfect reflectivity. We then compare the analytic and numerical predictions for echoes in real time, verifying their consistency. In particular, we find that the amplitudes of the first $\ensuremath{\sim}20$ echoes decay inversely with time, while the subsequent echoes decay exponentially. Finally, we present predictions for the signal-to-noise ratio of echoes for spinning BHs, which should be imminently detectable for massive remnants, subject to the uncertainty in the nonlinear initial conditions of the BH merger.

Gravitational wave echoes from black hole area quantization

Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Bekenstein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave “echoes” in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization.

Simple refutation of the Eppley–Hannah argument

In an influential paper, Eppley and Hannah argued that gravity must necessarily be quantized, by proposing a thought experiment involving classical gravitational waves interacting with quantum matter. They argue the interaction must either violate the uncertainty principle or allow superluminal signalling. The feasibility of implementing their experiment in our universe has been challenged by Mattingly, and other limitations of the argument have been noted by Huggett and Callender and by Albers et al. However, these critiques do not directly refute the claim that coupling quantum theories with a Copenhagen collapse postulate to unentanglable classical gravitational degrees of freedom leads to contradiction. I note here that if the gravitational field interacts with matter via the local quantum state, the Eppley–Hannah argument evidently fails. This seems a plausibly natural feature of a hybrid theory, whereas the alternative considered by Eppley–Hannah is evidently inconsistent with relativity.

Dark Energy and Inflation from Gravitational Waves

In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and “old cosmological constant” paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. Section 4 discusses the consistency of the theory with observational data on dark energy and inflation. The discussion of mechanism of acceleration and cosmological scenario are contained in Sections 5 and 6. Appendix contains the theory of stochastic nonlinear gravitational waves of arbitrary wavelength and amplitude in an isotropic Universe.

Cosmological acceleration from a scalar field and classical and quantum gravitational waves (Inflation and dark energy)

We show that on the average, homogeneous and isotropic scalar field and on the average homogeneous and isotropic ensembles of classical and quantum gravitational waves generate the de Sitter expansion of the empty (with no matter) space-time. At the start and by the end of its cosmological evolution the Universe is empty. The contemporary Universe is about 70% empty, so the effect of cosmological acceleration should be very noticeable. One can assume that it manifests itself as dark energy. At the start of the cosmological evolution, before the first matter was born, the Universe is also empty. The cosmological acceleration of such an empty space-time can manifests itself as inflation. To get the de Sitter accelerated expansion of the empty space-time under influence of scalar fields and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e. one needs to make a transition to the Euclidean space of imaginary time. One can assume that the very existence of inflation and dark energy could be considered as a possible observable evidence of the fact that time by its nature could be a complex value which manifests itself precisely at the start and by the end of the evolution of the Universe, i.e. in those periods when the Universe is empty (or nearly empty).

Gravicommunication, Subjectivity and Quantum Entanglement

In this work gravicommunication (GC) is introduced, as a new form of communication (different from the classical gravitational waves). GC involves gravitons (particles of gravitation) and manifests itself, particularly, in our subjective experiences. This research is based on quantum modification of the general relativity. The modification includes effects of production /absorption of gravitons, which turn out to have small, but finite mass and electric dipole moment. It is shown, that such gravitons form the dipole Bose-Einstein condensate, even for high temperature. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations. In this theory we got an interface between gravitons and ordinary matter, which very likely exist not only in cosmos, but everywhere, including our body and, especially, our brain. Subjective experiences are considered as a manifestation of that interface. A model of such interface is presented and some new experimentally verifiable aspects of natural neural systems are considered. According to the model, GC can be superluminal, which will solve the problem of quantum entanglement. Probable applications of these ideas include health (brain stimulation), new forms of communication, computational capabilities, energy resources and weapons. Some developed civilizations in the universe may already master GC (with various applications) and so should we.

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum and classical. We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form the de Sitter state of the empty homogeneous isotropic Universe. This state is the exact solution to the self-consistent equations of one-loop quantum gravity for gravitons in the empty FLRW space. It also is the exact solution to the self-consistent equations of back reaction for classical gravitational waves. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to make the transition to imaginary time and then come back to real time which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that the time was used as a complex variable, and this fact has a deep but still not understood meaning. De Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start and by the end of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^-5 is produced by fluctuations in the number of gravitons. The existence of a threshold and unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and De Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w>-1 for inflation and w<-1 for dark energy is consistent with observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy

10.1007/s11448-008-2001-9

An equation for the emission of classical gravitational waves due to quasi-elastic N → N particle scattering is derived in a model with compactified extra dimensions. In addition to previous classical studies, additional terms that are suppressed by factors of one over the frequency time compactification radius are also calculated. From this, a single formula is given which predicts the energy loss into the gravitational radiation from elastic collisions as well in the low-and high-energy limit.

Gravity waves signatures from anisotropic preinflation

We show that expanding or contracting Kasner universes are unstable due to the amplification of gravitational waves (GW). As an application of this general relativity effect, we consider a preinflationary anisotropic geometry characterized by a Kasner-like expansion, which is driven dynamically towards inflation by a scalar field. We investigate the evolution of linear metric fluctuations around this background, and calculate the amplification of the long-wavelength GW of a certain polarization during the anisotropic expansion (this effect is absent for another GW polarization, and for scalar fluctuations). These GW are superimposed to the usual tensor modes of quantum origin from inflation, and are potentially observable if the total number of inflationary $e$-folds exceeds the minimum required to homogenize the observable universe only by a small margin. Their contribution to the temperature anisotropy angular power spectrum decreases with the multipole $\ensuremath{\ell}$ as ${\ensuremath{\ell}}^{\ensuremath{-}p}$, where $p$ depends on the slope of the initial GW power spectrum. Constraints on the long-wavelength GW can be translated into limits on the total duration of inflation and the initial GW amplitude. The instability of classical GW (and zero-vacuum fluctuations of gravitons) during Kasner-like expansion (or contraction) may have other interesting applications. In particular, if GW become nonlinear, they can significantly alter the geometry before the onset of inflation.

Summary of the workshop: Classical general relativity and gravitational waves

In the workshop, classical general relativity and gravitational waves at ICGC-2007, eleven lectures were presented on classical general relativity and nine on gravitational waves. Lectures covered diverse topics in these areas during the three days of parallel sessions. We classify and summarize here the research work and results of the oral presentations made.

Classical gravitational radiation from quasi-elastic particle scattering in models with extra dimensions

An equation for the emission of classical gravitational waves due to quasi-elastic N → N particle scattering is derived in a model with compactified extra dimensions. In addition to previous classical studies, additional terms that are suppressed by factors of one over the frequency time compactification radius are also calculated. From this, a single formula is given which predicts the energy loss into the gravitational radiation from elastic collisions as well in the low-and high-energy limit.

On the interaction of mesoscopic quantum systems with gravity

AbstractWe review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non‐relativistic expansions of the Klein‐Gordon and Dirac equations in the post‐Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.

On the interaction of mesoscopic quantum systems with gravity

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non-relativistic expansions of the Klein-Gordon and Dirac equations in the post-Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.