Gravitational Memory Research Articles

Quantum probing of null singularities

We adapt the dual-null foliation to the functional Schr\"odinger representation of quantum field theory and study the behavior of quantum probes in plane-wave space-times near the null-singularity. A comparison between the Einstein-Rosen and the Brinkmann patch, where the latter extends beyond the first, shows a seeming tension that can be resolved by comparing the configuration spaces. Our analysis concludes that Einstein-Rosen space-times support exclusively configurations with non-empty gravitational memory that are focussed to a set of measure zero in the focal plane with respect to a Brinkmann observer. To conclude, we provide a rough framework to estimate the qualitative influence of back-reactions on these results.

Leveraging gravitational-wave memory to distinguish neutron star-black hole binaries from black hole binaries

In the observation of gravitational waves (GWs) from a compact binary coalescence system where the mass of one of the companions is $\leq 5~M_{\odot}$ the nature of the object is ambiguous until the measurements of tidal effects give evidence for the presence of a neutron star (NS) or a low mass black hole (BH). The relevance of tidal effects in a neutron star--black hole (NSBH) binary system depends crucially upon the mass and the spin of the companion BH. These effects become important predominantly when the binary system is of comparable mass and/or has large aligned spins. Depending upon the masses and spins the NS can even get tidally disrupted before the innermost stable circular orbit (ISCO) is reached. The gravitational-wave signatures of various tidal effects are encoded in the phasing of the signal and in the case of tidal disruption an abrupt cutoff of the signal amplitude occurs. In this work we show that tidal effects can also be captured by the nonlinear memory of the GW signal. Although small in amplitude, nonlinear memory is present at low frequency in contrast to the oscillatory GW signal. We introduce nonlinear memory in the NSBH and binary black hole (BBH) waveform models and show how the addition of memory aids in distinguishing NSBH systems from BBH systems for a larger part of the parameter space. We discuss the recently detected events of interest by LIGO-Virgo and provide the future prospects for the third generation detectors where nonlinear memory can play a crucial role in inferring the nature of the coalescence as BBH or NSBH from its GW signal alone.

Did Goryachev et al. detect megahertz gravitational waves?

Goryachev et al. [1] recently announced the detection of "two strongly significant events" in their Bulk Acoustic Wave High Frequency Gravitational Wave Antenna. They claim many possibilities for the cause of these events, including high-frequency megahertz gravitational waves. We demonstrate these events are not due to gravitational waves for two reasons. 1) The inferred stochastic gravitational-wave background from these events implies the gravitational-wave energy density of the Universe is $\Omega_{\rm gw}\approx 10^8$, approximately $10^8$ times the closure density of the Universe. 2) The low-frequency gravitational-wave memory signal that accompanies any high-frequency gravitational-wave source visible by the current generation of high-frequency detectors would have been visible by LIGO/Virgo as a transient burst with signal-to-noise ratio $\gtrsim10^6$. The non-detection of such loud memory bursts throughout the operation of LIGO/Virgo rules out the gravitational-wave explanation for the high-frequency events detected by Goryachev et al. We discuss broader implications of this work for the ongoing experimental search for ultra high-frequency (MHz-GHz) gravitational waves.

Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation

Gravitational-wave (GW) memory effects produce permanent shifts in the GW strain and its time integrals after the passage of a burst of GWs. Their presence is closely tied to symmetries of asymptotically flat spacetimes and fluxes of conserved charges conjugate to these symmetries. While the phenomenology of GW memory effects is well understood in general relativity (GR), it is less well understood in the many modifications to GR. We recently computed asymptotically flat solutions, symmetries, conserved quantities, and GW memory effects in one such modified theory: Brans-Dicke theory. In this paper, we apply our results from this earlier work to compute the GW memories from compact binaries in the post-Newtonian (PN) approximation. In addition to taking the PN limit of these effects, we work in the approximation that the energy and angular momentum losses through scalar radiation are small compared to the energy and angular momentum losses through (tensor) GWs. We focus on the tensor (as opposed to scalar) GW memory effect, which we compute through Newtonian order, and the small differences induced by scalar radiation at this order. Specifically, we compute the nonlinear parts of the tensor displacement and spin GW memory effects produced during the inspiral of quasicircular, nonprecessing binaries in Brans-Dicke theory. Because the energy radiated through the scalar dipole moment appears as a -1 PN order-effect, then in this approximation, the displacement memory has a logarithmic dependence on the PN parameter and the spin memory has a relative -1 PN-order correction; these corrections are ultimately small because they are related to the total energy and angular momentum radiated in the scalar field, respectively. At Newtonian order, the scalar radiation also gives rise to a sky pattern of the memory effect around an isolated source that differs from that of the memory effect in GR.

Quantum imprints of gravitational shockwaves

Gravitational shockwaves are simple exact solutions of Einstein equations representing the fields of ultrarelativistic sources and idealized gravitational waves (shocks). Historically, much work has focused on shockwaves in the context of possible black hole formation in high energy particle collisions, yet they remain at the forefront of research even today. Representing hard modes in the bulk, shocks give rise to the gravitational memory effect at the classical level and implant supertranslation (BMS) hair onto a classical spacetime at the quantum level. The aim of this paper is to further our understanding of the ‘information content’ of such supertranslations. Namely, we show that, contrary to the several claims in the literature, a gravitational shockwave does leave a quantum imprint on the vacuum state of a test quantum field and that this imprint is accessible to local observers carrying Unruh-DeWitt (UDW) detectors in this spacetime.

Impact of Dynamic LED Non-Linearity on DCO-OFDM Optical Wireless Communication

DC-Offset Orthogonal Frequency Division Multiplexing (DCO-OFDM) is a popular modulation method for Optical Wireless Communication (OWC) as it can assign specific power levels and constellations to different subcarrier frequencies across the low-pass response of the LED. However, LEDs exhibit dynamic non-linearities to which OFDM is very sensitive. As LED signals are subject to non-linear memory effects in photon generation, different OFDM subcarriers experience different amounts of distortion. This letter translates the LED behavior into a communication channel model for OFDM modulation. It gives an experimentally verified expression for the Signal-to-Distortion Ratio (SDR) as it varies per subcarrier in OFDM systems.

Light speed memory as a local observable for soft hairs

Einstein observers in flat space-time are inertial observers which use light to synchronize their clocks. For such observers, speed of light is a constant by construction. However, one can use super-translations to change coordinates from Einstein to BMS coordinates. From the point of view of BMS observers, speed of light is not a constant all over the space-time and in all directions. So in general, clocks which are synchronized for Einstein observers are not synchronized for BMS observers, and vice versa. Based on this fact, we propose a local observable for detecting the soft hairs, which is the variations in speed of light for such observers. We also investigate the relation of this observable to gravitational memory, which is a permanent change of position of test particles at infinity, after a gravitational wave passes completely from them. It is shown that the BMS time coordinate is the physical time after a gravitational wave, and it is the legitimate time to be used to calculate the light speed. Based on this argument, the analysis predicts a permanent change in the speed of light rays which propagate in asymptotics after a gravitational wave. Moreover, it is explained how this change is related to the gravitational memory by comparing their significance in observations.

Gravitational wave memory of the binary black hole events in GWTC-2

Gravitational wave (GW) memory is an important prediction of general relativity. Existing works on the GW memory detection targeted the nonoscillatory strain. It is hard for the wave strain analysis method to detect the GW memory due to its quasidirect current behavior and weakness. We implement a completely different scheme in this work to estimate the GW memory. In this scheme, we first apply the Bondi-Metzner-Sachs method to calculate the GW memory of a binary black hole based on numerical relativity simulation. Then we construct a surrogate model to relate a binary black hole's parameters and the GW memory. Afterwards we apply this surrogate model together with Bayesian techniques to estimate the GW memory of the 48 binary black hole events recorded in GWTC-2. The GW memory corresponding to all 48 events has been estimated.

New general decay result for a class of neutral viscoelastic equations

We are concerned with the decay estimate of a neutral viscoelastic equation with nonlinear boundary damping and boundary memory effect. We obtain a general decay theorem for the neutral viscoelastic equation by showing that its system energy is controlled by a solution of the associated ODE. Moreover, distinguished from the previous compactness-uniqueness method, we propose an analytical approach to estimate the low-order terms by using the Sobolev imbedding theory.

First-order velocity memory effect from compact binary coalescing sources

It has long been known that gravitational waves from compact binary coalescing sources are responsible for a first-order displacement memory effect experienced by a pair of freely falling test masses. This constant displacement is sourced from the non-vanishing final gravitational-wave strain present in the wave's after-zone, often referred to as the non-linear memory effect, and is of the same order of magnitude as the strain from the outgoing quadrupole radiation. Hence, this prediction of general relativity is verifiable experimentally by measurement of the final relative separation between test masses that comprise gravitational-wave detectors. In a separate context, independent calculations have demonstrated that exact, sandwich, plane wave spacetimes exhibit a velocity memory effect: a non-zero relative velocity, gained by a pair of test masses in free fall, after the passage of a gravitational wave. In this paper, we find that in addition to the known constant displacement memory effect test masses experience, a velocity memory effect at leading order arises due to the non-linear nature of gravitational waves from compact binary sources. We discuss the magnitude of the first-order velocity memory effect in the context of observing gravitational-wave radiation from super massive binary black hole mergers in LISA.

Boosted Model Tree-Based Behavioral Modeling for Digital Predistortion of RF Power Amplifiers

In this article, we propose a new behavioral modeling approach, called boosted model tree, to characterize and compensate for the complex nonlinear distortions induced by wideband high-efficiency radio frequency power amplifiers. With the proposed model, the input data are classified into different zones by decision trees and each zone is assigned separate submodels. We also employ a model boosting technique to build multiple parallel tree structures that jointly model the desired nonlinear behavior. By designing dedicated optimization procedures, both tree structures and submodel coefficients can be efficiently identified. It is demonstrated that the combination of piecewise and parallel structures provides a powerful and hardware-efficient way to model nonlinear memory effect and cross terms. Based on the experimental results, the proposed method can achieve improved linearization performance with low hardware complexity under challenging wideband predistortion scenarios.

Nonlinear gravitational-wave memory from cusps and kinks on cosmic strings

The nonlinear memory effect is a fascinating prediction of general relativity (GR), in which oscillatory gravitational-wave (GW) signals are generically accompanied by a monotonically-increasing strain which persists in the detector long after the signal has passed. This effect is directly accessible to GW observatories, and presents a unique opportunity to test GR in the dynamical and nonlinear regime. In this article we calculate, for the first time, the nonlinear memory signal associated with GW bursts from cusps and kinks on cosmic string loops, which are an important target for current and future GW observatories. We obtain analytical waveforms for the GW memory from cusps and kinks, and use these to calculate the ‘memory of the memory’ and other higher-order memory effects. These are among the first memory observables computed for a cosmological source of GWs, with previous literature having focused almost entirely on astrophysical sources. Surprisingly, we find that the cusp GW signal diverges for sufficiently large loops, and argue that the most plausible explanation for this divergence is a breakdown in the weak-field treatment of GW emission from the cusp. This shows that previously-neglected strong gravity effects must play an important rôle near cusps, although the exact mechanism by which they cure the divergence is not currently understood. We show that one possible resolution is for these cusps to collapse to form primordial black holes (PBHs); the kink memory signal does not diverge, in agreement with the fact that kinks are not predicted to form PBHs. Finally, we investigate the prospects for detecting memory from cusps and kinks with current and future GW observatories, considering both individual memory bursts and the contribution of many such bursts to the stochastic GW background. We find that in the scenario where the cusp memory divergence is cured by PBH formation, the memory signal is strongly suppressed and is not likely to be detected. However, alternative resolutions of the cusp divergence may in principle lead to much more favourable observational prospects.

Definitions of angular momentum and super angular momentum in asymptotically flat spacetimes: Properties and applications to compact-binary mergers

The symmetries of asymptotically flat spacetimes in general relativity are given by the Bondi-Metzner-Sachs (BMS) group, though there are proposed generalizations of its symmetry algebra. Associated with each symmetry is a charge and a flux, and the values of these charges and their changes can characterize a spacetime. The charges of the BMS group are relativistic angular momentum and supermomentum (which includes four-momentum); the extensions of the BMS algebra also include generalizations of angular momentum called ``super angular momentum.'' Several different formalisms have been used to define angular momentum, and they produce nonequivalent expressions for the charge. It was shown recently that these definitions can be summarized in a two-parameter family of angular momenta, which we investigate in this paper. We find that requiring that the angular momentum vanishes in flat spacetime restricts the two parameters to be equal. If we do not require that the angular momentum agrees with a common Hamiltonian definition, then we are left with a one-parameter family of angular momenta that includes the definitions from the several different formalisms. We then also propose a similar two-parameter family of super angular momentum. We examine the effect of the free parameters on the values of the angular momentum and super angular momentum from nonprecessing binary-black-hole mergers. The definitions of angular momentum differ at a high post-Newtonian order for these systems, but only when the system is radiating gravitational waves (not before and after). The different super-angular-momentum definitions occur at lower orders, and there is a difference in the change of super angular momentum even after the gravitational waves pass, which arises because of the gravitational-wave memory effect. We estimate the size of these effects using numerical-relativity surrogate waveforms and find they are small but resolvable.

Memory remains undetected: Updates from the second LIGO/Virgo gravitational-wave transient catalog

The LIGO and Virgo observatories have reported 39 new gravitational-wave detections during the first part of the third observation run, bringing the total to 50. Most of these new detections are consistent with binary black-hole coalescences, making them suitable targets to search for gravitational-wave memory, a nonlinear effect of general relativity. We extend a method developed in previous publications to analyze these events to determine a Bayes factor comparing the memory hypothesis to the no-memory hypothesis. Specifically, we calculate Bayes factors using two waveform models with higher-order modes that allow us to analyze events with extreme mass ratios and precessing spins, both of which have not been possible before. Depending on the waveform model, we find a combined $\mathrm{ln}{\mathrm{BF}}_{\mathrm{mem}}=0.024$ or $\mathrm{ln}{\mathrm{BF}}_{\mathrm{mem}}=0.049$ in favor of memory. This result is consistent with recent predictions that indicate $\mathcal{O}(2000)$ binary black-hole detections will be required to confidently establish the presence or absence of memory.

The neutrino gravitational memory from a core collapse supernova: phenomenology and physics potential

General Relativity predicts that the passage of matter or radiation from an asymmetrically-emitting source should cause a permanent change in the local space-time metric. This phenomenon, called the gravitational memory effect, has never been observed, however supernova neutrinos have long been considered a promising avenue for its detection in the future. With the advent of deci-Hertz gravitational wave interferometers, observing the supernova neutrino memory will be possible, with important implications for multimessenger astronomy and for tests of gravity. In this work, we develop a phenomenological (analytical) toy model for the supernova neutrino memory effect, which is overall consistent with the results of numerical simulations. This description is then generalized to several case studies of interest. We find that, for a galactic supernova, the dimensionless strain, h(t), is of order ∼ 10-22 - 10-21, and develops over a typical time scale that varies between ∼ 0.1 - 10 s, depending on the time-evolution of the anisotropy of the neutrino emission. The characteristic strain, h c(f), has a maximum at a frequency f max ∼ \U0001d4aa(10-1) - \U0001d4aa(1) Hz. The detailed features of the time- and frequency-structure of the memory strain will inform us of the matter dynamics near the collapsed core, and allow to distinguish between different stellar collapse scenarios. Next generation gravitational wave detectors like DECIGO and BBO will be sensitive to the neutrino memory effect for supernovae at typical galactic distances and beyond; with Ultimate DECIGO exceeding a detectability distance of 10 Mpc.

Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries, and gravitational-wave memory effects

Gravitational-wave memory effects are identified by their distinctive effects on families of freely falling observers: after a burst of waves pass by their locations, memory effects can cause lasting relative displacements of the observers. These effects are closely related to the infrared properties of gravity and other massless field theories, including their asymptotic symmetries and conserved quantities. In this paper, we investigate the connection between memory effects, symmetries, and conserved quantities in Brans-Dicke theory. We compute the field equations in Bondi coordinates, and we define a set of boundary conditions that represent asymptotically flat solutions in this context. Next, we derive the asymptotic symmetry group of these spacetimes, and we find that it is the same as the Bondi-Metzner-Sachs group in general relativity. Because there is an additional polarization of gravitational waves in Brans-Dicke theory, we compute the memory effects associated with this extra polarization (the so-called "breathing" mode). This breathing mode produces a uniform expansion (or contraction) of a ring of freely falling observers. After these breathing gravitational waves pass by the observers' locations, there are two additional memory effects that depend on their initial displacements and relative velocities. Neither of these additional memory effects seems to be related to asymptotic symmetries or conserved quantities; rather, they are determined by the properties of the nonradiative region before and after the bursts of the scalar field and the gravitational waves. We discuss the properties of these regions necessary to support nontrivial breathing-mode-type memory effects.

Gravitational breathing memory and dual symmetries

Brans-Dicke theory contains an additional propagating mode which causes homogeneous expansion and contraction of test bodies in transverse directions. This “breathing” mode is associated with novel memory effects in addition to those of general relativity. Standard tensor mode memories are related to a symmetry principle: they are determined by the balance equations corresponding to the BMS symmetries. In this paper, we show that the leading and subleading breathing memory effects are determined by the balance equations associated with the leading and “overleading” asymptotic symmetries of a dual formulation of the scalar field in terms of a two-form gauge field. The memory effect causes a transition in the vacuum of the dual gauge theory. These results highlight the significance of dual charges and the physical role of overleading asymptotic symmetries.

Digital Predistortion of Wideband Signals with Reduced Complexity Based on Feedback Wiener System

Digital predistortion (DPD) using baseband signals is commonly used for power amplifier linearization. This paper is devoted to this subject and aims to reduce DPD complexity. In this study, we propose a structure that allows to decrease the number of DPD parameters by using multiple blocks, with each one of them dedicated to characterizing the non-linear behavior and/or memory effects. Such a structure is based on the feedback Wiener system, involving a FIR filter used as a feedback path to reproduce the PA inverse dynamics. A memory polynomial block (MP) is inserted as the final element to minimize the modeling errors. A relevant model identification method, based on an iterative algorithm, has been developed as well. The proposed architecture is used for the linearization of a commercial class-AB LDMOS RF PA by NXP Semiconductors, in wideband communication systems. Comparison of performance with the conventional generalized memory polynomial model (GMP) shows that the proposed model offers similar results, with its advantage consisting in the reduced number of parameters.

Gaussian Pulse Characterization of RF Power Amplifiers

This work presents a new RF power amplifier characterization technique based on a Gaussian pulse, which is shown to approximate the envelope of a multicarrier signal with 0.5% error around the peaks. The standard deviation of the Gaussian pulses is inversely proportional to the I/Q signal bandwidth. This test signal is shown to accurately capture nonlinear memory effects that result in gain dispersion after the peak power is reached. As an example, it is shown that the gain amplitude and phase can vary up to 2.3 dB and 6° for a 10-W 3.75-GHz GaN power-amplifier evaluation board, depending on the I/Q signal bandwidth and peak power level.

A gravitational non-radiative memory effect

We revisit the issue of memory effects, i.e. effects giving rise to a net cumulative change of the configuration of test particles, using a toy model describing the emission of radiation by a compact source and focusing on the scalar, hence non-radiative, part of the Riemann curvature. Motivated by the well known fact that gravitational radiation is accompanied by a memory effect, i.e. a permanent displacement of the relative separation of test particles, present after radiation has passed, we investigate the existence of an analog effect in the non-radiative part of the gravitational field. While quadrupole and higher multipoles undergo oscillations responsible for gravitational radiation, energy, momentum and angular momentum are conserved charges undergoing non-oscillatory change due to radiation emission. We show how the source re-arrangement due to radiation emission produce time-dependent scalar potentials which induce a time variation in the scalar part of the Riemann curvature tensor. As a result, on general grounds a velocity memory effect appears, depending on the inverse of the square of the distance of the observer from the source, thus making it almost impossible to observe, as shown by comparison to the planned gravitational detector noise spectral densities.