New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms

Algorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals.

Gravitational-wave asteroseismology with fundamental modes from compact binary inspirals

Gravitational waves (GWs) from binary neutron stars encode unique information about ultra-dense matter through characterisic signatures associated with a variety of phenomena including tidal effects during the inspiral. The main tidal signature depends predominantly on the equation of state (EoS)-related tidal deformability parameter Λ, but at late times is also characterised by the frequency of the star's fundamental oscillation mode (f-mode). In General Relativity and for nuclear matter, Λ and the f-modes are related by universal relations which may not hold for alternative theories of gravity or exotic matter. Independently measuring Λ and the f-mode frequency enables tests of gravity and the nature of compact binaries. Here we present directly measured constraints on the f-mode frequencies of the companions of GW170817. We also show that future GW detector networks will measure f-mode frequencies to within tens of Hz, enabling precision GW asteroseismology with binary inspiral signals alone.

Posterior samples of the parameters of binary black holes from Advanced LIGO, Virgo's second observing run

This paper presents a parameter estimation analysis of the seven binary black hole mergers-GW170104, GW170608, GW170729, GW170809, GW170814, GW170818, and GW170823-detected during the second observing run of the Advanced LIGO and Virgo observatories using the gravitational-wave open data. We describe the methodology for parameter estimation of compact binaries using gravitational-wave data, and we present the posterior distributions of the inferred astrophysical parameters. We release our samples of the posterior probability density function with tutorials on using and replicating our results presented in this paper.

A ring-like accretion structure in M87 connecting its black hole and jet

The nearby radio galaxy M87 is a prime target for studying black hole accretion and jet formation1,2. Event Horizon Telescope observations of M87 in 2017, at a wavelength of 1.3 mm, revealed a ring-like structure, which was interpreted as gravitationally lensed emission around a central black hole3. Here we report images of M87 obtained in 2018, at a wavelength of 3.5 mm, showing that the compact radio core is spatially resolved. High-resolution imaging shows a ring-like structure of [Formula: see text] Schwarzschild radii in diameter, approximately 50% larger than that seen at 1.3 mm. The outer edge at 3.5 mm is also larger than that at 1.3 mm. This larger and thicker ring indicates a substantial contribution from the accretion flow with absorption effects, in addition to the gravitationally lensed ring-like emission. The images show that the edge-brightened jet connects to the accretion flow of the black hole. Close to the black hole, the emission profile of the jet-launching region is wider than the expected profile of a black-hole-driven jet, suggesting the possible presence of a wind associated with the accretion flow.

Cosmology in the mimetic higher-curvature [Formula: see text] gravity

In the framework of the mimetic approach, we study the [Formula: see text] gravity with the Lagrange multiplier constraint and the scalar potential. We introduce field equations for the discussed theory and overview their properties. By using the general reconstruction scheme we obtain the power law cosmology model for the [Formula: see text] case as well as the model that describes symmetric bounce. Moreover, we reconstruct model, unifying both matter dominated and accelerated phases, where ordinary matter is neglected. Using inverted reconstruction scheme we recover specific [Formula: see text] function which give rise to the de-Sitter evolution. Finally, by employing the perfect fluid approach, we demonstrate that this model can realize inflation consistent with the bounds coming from the BICEP2/Keck array and the Planck data. We also discuss the holographic dark energy density in terms of the presented [Formula: see text] theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.

Emergence of Calabi-Yau manifolds in high-precision black-hole scattering

When two massive objects (black holes, neutron stars or stars) in our universe fly past each other, their gravitational interactions deflect their trajectories1,2. The gravitational waves emitted in the related bound-orbit system-the binary inspiral-are now routinely detected by gravitational-wave observatories3. Theoretical physics needs to provide high-precision templates to make use of unprecedented sensitivity and precision of the data from upcoming gravitational-wave observatories4. Motivated by this challenge, several analytical and numerical techniques have been developed to approximately solve this gravitational two-body problem. Although numerical relativity is accurate5-7, it is too time-consuming to rapidly produce large numbers of gravitational-wave templates. For this, approximate analytical results are also required8-15. Here we report on a new, highest-precision analytical result for the scattering angle, radiated energy and recoil of a black hole or neutron star scattering encounter at the fifth order in Newton's gravitational coupling G, assuming a hierarchy in the two masses. This is achieved by modifying state-of-the-art techniques for the scattering of elementary particles in colliders to this classical physics problem in our universe. Our results show that mathematical functions related to Calabi-Yau (CY) manifolds, 2n-dimensional generalizations of tori, appear in the solution to the radiated energy in these scatterings. We anticipate that our analytical results will allow the development of a new generation of gravitational-wave models, for which the transition to the bound-state problem through analytic continuation and strong-field resummation will need to be performed.

Measurement of the Weyl potential evolution from the first three years of dark energy survey data

The Weyl potential, which is the sum of the spatial and temporal distortions of the Universe's geometry, provides a direct way of testing the theory of gravity and the validity of the ΛCDM (Lambda Cold Dark Matter) model. Here we present measurement of the Weyl potential at four redshifts bins using data from the first three years of observations of the Dark Energy Survey. We find that the measured Weyl potential is 2 σ, respectively 2.8 σ, below the ΛCDM predictions in the two lowest redshift bins. We show that these low values of the Weyl potential are at the origin of the tension between Cosmic Microwave Background measurements and weak lensing measurements, regarding the parameter σ8 which quantifies the clustering of matter. Interestingly, we find that the tension remains if no information from the Cosmic Microwave Background is used. Dark Energy Survey data on their own prefer a high value of the primordial fluctuations, together with a slow evolution of the Weyl potential. An important feature of our method is that the measurements of the Weyl potential are model-independent and can therefore be confronted with any theory of gravity, allowing efficient tests of models beyond General Relativity.

The multi-mode acoustic gravitational wave experiment: MAGE

The Multi-mode Acoustic Gravitational wave Experiment (MAGE) is a high frequency gravitational wave detection experiment. In its first stage, the experiment features two near-identical quartz bulk acoustic wave resonators that act as strain antennas with spectral sensitivity as low as 6.6 × 10-21 [strain]/[Formula: see text] in multiple narrow bands across MHz frequencies. MAGE is the successor to the initial path-finding experiments; GEN 1 and GEN 2. These precursor runs demonstrated the successful use of the technology, employing a single quartz gravitational wave detector that found significantly strong and rare transient features. As the next step to this initial experiment, MAGE will employ further systematic rejection strategies by adding an additional quartz detector such that localised strains incident on just a single detector can be identified. The primary goals of MAGE will be to target signatures arising from objects and/or particles beyond that of the standard model, as well as identifying the source of the rare events seen in the predecessor experiment. The experimental set-up, current status and future directions for MAGE are discussed. Calibration procedures of the detector and signal amplification chain are presented. The sensitivity of MAGE to gravitational waves is estimated from knowledge of the quartz resonators. Finally, MAGE is assembled and tested in order to determine the thermal state of its new components.

Lense-Thirring precession after a supermassive black hole disrupts a star

An accretion disk formed around a supermassive black hole after it disrupts a star is expected to be initially misaligned with respect to the equatorial plane of the black hole. This misalignment induces relativistic torques (the Lense-Thirring effect) on the disk, causing the disk to precess at early times, whereas at late times the disk aligns with the black hole and precession terminates1,2. Here we report, using high-cadence X-ray monitoring observations of a tidal disruption event (TDE), the discovery of strong, quasi-periodic X-ray flux and temperature modulations. These X-ray modulations are separated by roughly 15 days and persist for about 130 days during the early phase of the TDE. Lense-Thirring precession of the accretion flow can produce this X-ray variability, but other physical mechanisms, such as the radiation-pressure instability3,4, cannot be ruled out. Assuming typical TDE parameters, that is, a solar-like star with the resulting disk extending at most to the so-called circularization radius, and that the disk precesses as a rigid body, we constrain the disrupting dimensionless spin parameter of the black hole to be 0.05 ≲ ∣a∣ ≲ 0.5.

Real-time inference for binary neutron star mergers using machine learning

Mergers of binary neutron stars emit signals in both the gravitational-wave (GW) and electromagnetic spectra. Famously, the 2017 multi-messenger observation of GW170817 (refs. 1,2) led to scientific discoveries across cosmology3, nuclear physics4-6 and gravity7. Central to these results were the sky localization and distance obtained from the GW data, which, in the case of GW170817, helped to identify the associated electromagnetic transient, AT 2017gfo (ref. 8), 11 h after the GW signal. Fast analysis of GW data is critical for directing time-sensitive electromagnetic observations. However, owing to challenges arising from the length and complexity of signals, it is often necessary to make approximations that sacrifice accuracy. Here we present a machine-learning framework that performs complete binary neutron star inference in just 1 s without making any such approximations. Our approach enhances multi-messenger observations by providing: (1) accurate localization even before the merger; (2) improved localization precision by around 30% compared to approximate low-latency methods; and (3) detailed information on luminosity distance, inclination and masses, which can be used to prioritize expensive telescope time. Additionally, the flexibility and reduced cost of our method open new opportunities for equation-of-state studies. Finally, we demonstrate that our method scales to long signals, up to an hour in length, thus serving as a blueprint for data analysis for next-generation ground- and space-based detectors.

Correlation between birefringence and absorption mapping in large-size Sapphire substrates for gravitational-wave interferometry

In high-sensitive laser interferometers, such as the gravitational-wave detector KAGRA, ultra-high-quality mirrors are essential. In the case of KAGRA, where cavity mirrors are cooled down to 20 K, large-size Sapphire crystals are used as the substrate for the main mirrors to achieve both a good optical quality (i.e., low absorption and uniform refractive index) and optimized thermal behavior under cryogenic temperatures. To implement the very tight optical specifications required by this demanding application, it is mandatory to test the optical homogeneity of different substrates. In order to characterize refractive-index inhomogeneities of large-size uniaxial samples such as the KAGRA Sapphire test masses, we developed a dedicated setup, allowing to resolve birefringence changes with a sensitivity in the order of [Formula: see text] and a spatial resolution of [Formula: see text]. Moreover, the same setup allows us to simultaneously record residual absorption maps, thus allowing for a comparison between birefringence and absorption features. In this paper, we will present for the first time measurements on a KAGRA-sized Sapphire substrate which has been characterized in terms of absorption already in an earlier work. Both birefringence inhomogeneities and absorption distributions will be compared and correlations discussed.

Pinpointing gravitational waves via astrometric gravitational wave antennas

The direct detection of gravitational waves by ground-based optical interferometers has opened a new window in astronomy. Besides, the sensitivity of these linear detectors to the direction of arrival of an incoming gravitational wave is limited compared to current prospects of high-precision, space-based, astrometry. Indeed, advanced methods of differential relativistic astrometry offer a unique opportunity to overcome that situation. Here, we present a novel concept for a gravitational wave antenna that uses angles between close pairs of point-like sources as natural (angular) "arms" to characterise the very tiny variations in angular separations induced by a passing gravitational wave. The proposed new astrometric gravitational wave observable proves to be a powerful tool to substantially enhance the effect of gravitational waves of different strengths by exploiting optical resolution to the fullest. Then, by optically multiplexing three (or more) of such astrometric "arms", it would be also possible to pinpoint source directions to unprecedented levels.

Detecting single gravitons with quantum sensing

The quantization of gravity is widely believed to result in gravitons - particles of discrete energy that form gravitational waves. But their detection has so far been considered impossible. Here we show that signatures of single graviton exchange can be observed in laboratory experiments. We show that stimulated and spontaneous single-graviton processes can become relevant for massive quantum acoustic resonators and that stimulated absorption can be resolved through continuous sensing of quantum jumps. We analyze the feasibility of observing the exchange of single energy quanta between matter and gravitational waves. Our results show that single graviton signatures are within reach of experiments. In analogy to the discovery of the photo-electric effect for photons, such signatures can provide the first experimental clue of the quantization of gravity.

Three-dimensional wormhole with cosmic string effects on eigenvalue solution of non-relativistic quantum particles

In this paper, we explore the quantum system of non-relativistic particles in a unique scenario: a circularly symmetric and static three-dimensional wormhole space-time accompanied by cosmic strings. We focus on a specific case where the redshift function [Formula: see text] to be zero and defining the shape function as [Formula: see text]. After establishing this background space-time, we investigate the behavior of a harmonic oscillator within the same wormhole context. By doing so, we observe the effects of the cosmic string and wormhole throat radius on the eigenvalue solution of the oscillator's eigenvalue problem. The primary finding is that these cosmic features lead to modifications in the energy spectrum and wave functions of the system, breaking the degeneracy of energy levels that would typically be present in a more conventional setting. As a particular case, we present the specific energy level [Formula: see text] and the corresponding wave function [Formula: see text], which are associated with the ground state of the quantum system. These results highlight the fascinating and unique properties of the harmonic oscillator in the background of a circularly symmetric, static wormhole space-time with cosmic strings.

Explicit construction of Penrose diagrams for black hole to white hole transition with spacelike thin shells

In this article, we explicitly construct the coordinates associated with the Penrose diagram in spacetimes connected via a spacelike thin shell in the following two examples: the generalized black-to-white hole bounce with mass difference and the Schwarzschild-to-de Sitter transition. We point out the issue of the first junction condition in the Penrose diagram constructed by cutting and pasting analytically known metrics with spherical symmetry by a static spacelike thin shell. With the goal of a global conformal coordinate chart associated with the corresponding Penrose diagram without discontinuity at the thin shell, we give a procedure consisting of three conformal transformations that serve different purposes. The first two of them are used to generate a continuous coordinate patch covering the entire thin shell, and therefore, the Penrose diagram can be constructed properly by patches with overlapping. The third transformation removes any coordinate singularity reintroduced by the first two transformations at the event horizons.

Embedding diagrams in stationary spacetimes

We find the spatial and dynamic embedding diagrams in stationary black hole spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared through their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes, and compare them with the dynamic embedding diagram of Schwarzschild spacetime.

Quasinormal modes and shadow of noncommutative black hole

In this paper we investigate quasinormal modes (QNM) for a scalar field around a noncommutative Schwarzschild black hole. We verify the effect of noncommutativity on quasinormal frequencies by applying two procedures widely used in the literature. The first is the Wentzel-Kramers-Brillouin (WKB) approximation up to sixth order. In the second case we use the continuous fraction method developed by Leaver. Besides, we also show that due to noncommutativity, the shadow radius is reduced when we increase the noncommutative parameter. In addition, we find that the shadow radius is nonzero even at the zero mass limit for finite noncommutative parameter.