Gravitational Memory Research Articles

Inferring the gravitational wave memory for binary coalescence events

Full, non-linear general relativity predicts a memory effect for gravitational waves. For compact binary coalescence, the total gravitational memory serves as an inferred observable, conceptually on the same footing as the mass and the spin of the final black hole. Given candidate waveforms for any LIGO event, then, one can calculate the posterior probability distribution functions for the total gravitational memory, and use them to compare and contrast the waveforms. In this paper we present these posterior distributions for the binary black hole merger events reported in the first Gravitational Wave Transient Catalog (GWTC-1), using the Phenomenological and Effective-One-Body waveforms. On the whole, the two sets of posterior distributions agree with each other quite well though we find larger discrepancies for the $\ell=2, m=1$ mode of the memory. This signals a possible source of systematic errors that was not captured by the posterior distributions of other inferred observables. Thus, the posterior distributions of various angular modes of total memory can serve as diagnostic tools to further improve the waveforms. Analyses such as this would be valuable especially for future events as the sensitivity of ground based detectors improves, and for LISA which could measure the total gravitational memory directly.

Accurate calculation of gravitational wave memory

Gravitational wave memory is an important prediction of general relativity. The detection of the gravitational wave memory can be used to test general relativity and deduce the property of the gravitational wave source. A quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory have always used the energy flux of the gravitational wave to calculate the memory. Accurately calculating the memory is highly demanded. Here we apply the Bondi-Metzner-Sachs method to calculate the gravitational wave memory. Our method does not need slow motion and weak field conditions for the gravitational wave source. This method can accurately calculate the memory if the nonmemory waveform is known. As an example, we combine our method with the matured numerical relativity result of a nonmemory waveform for binary black hole coalescence. We calculate the waveform for the memory which can be used to aid memory detection and help us understand the gravitational wave source. Our calculation result is consistent with the numerical relativity result of memory. We determine the dependence of the memory amplitude on the mass ratio and the spins of the two spin-aligned black holes.

New effects in gravitational waves and memory

We find new effects for gravitational waves and memory in asymptotically flat spacetimes of slow decay. In particular, we find growing magnetic memory for these general systems. These effects do not arise in spacetimes resulting from data with fast decay towards infinity, including data that is stationary outside a compact set. The new results are derived for the Einstein vacuum as well as for the Einstein-null-fluid equations describing neutrino radiation, where the neutrino distribution falls off slowly towards infinity. Moreover, they hold for other matter and energy fields coupled to the Einstein equations as long as the data obey corresponding decay laws and other conditions are fulfilled. The magnetic memory occurs naturally in the Einstein vacuum regime of pure gravitation, and in the Einstein-matter systems satisfying the aforementioned conditions. As a main new effect, we find that there is diverging magnetic memory sourced by the magnetic part of the curvature. In the most extreme case, the magnetic memory, in addition, features a curl term from the neutrino cloud, growing at the same rate. Electric memory is diverging as well, sourced by the electric part of the curvature tensor and the corresponding energy-momentum component. Shear (news) adds to the electric memory. Moreover, a multitude of lower order terms contribute to both electric and magnetic memory. It has been known that for stronger decay of the data, including data that is stationary outside a compact set, gravitational wave memory is finite and of electric parity only. The more general scenarios in this article exhibit richer structures displaying the physics of these more general systems. We lay open these new structures. Further, we identify a range of decay rates for asymptotically flat spacetimes for which the new effects occur but with different leading order behavior. The new effects are expected to be seen in current and future gravitational wave detectors. They have an abundance of applications of which we mention a few in this paper. Applications include exploring gravitational wave sources of the above types, detecting dark matter via gravitational waves and other areas of physics.

Adding gravitational memory to waveform catalogs using BMS balance laws

Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can correct the strain waveforms in the SXS catalog to include the missing displacement memory. Our results show that these corrected waveforms satisfy the BMS balance laws to a much higher degree of accuracy. Furthermore, we find that these corrected strain waveforms coincide especially well with the waveforms obtained from Cauchy-characteristic extraction (CCE) that already exhibit memory effects. These corrected strain waveforms also evade the transient junk effects that are currently present in CCE waveforms. Lastly, we make our code for computing these contributions to the BMS balance laws and memory publicly available as a part of the python package $\texttt{sxs}$, thus enabling anyone to evaluate the expected memory effects and violation of the BMS balance laws.

Gravitational memory effects in Brans‐Dicke theory

There exist gravitational memory effects in Brans‐Dicke theory. They are closely related to the Bondi‐Metzner‐Sachs symmetries present on the null infinity in an isolated system. By studying the asymptotically flat spacetime in Brans‐Dicke theory and the asymptotic symmetries, one discovers that the displacement memory effect in the tensor sector is due to the vacuum transition caused by the null energy fluxes penetrating the null infinity, while in the scalar sector, the vacuum transition is due to the angular momentum fluxes. Together with the spin and the center‐of‐mass memory effects, the displacement memories are constrained by various flux‐balance laws.

Gravitational memory effects and Bondi-Metzner-Sachs symmetries in scalar-tensor theories

The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetries of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinite dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors in the scalar-tensor theory. The supertranslation relates the vacua in the tensor sector, while in the scalar sector, it is the Lorentz transformation that transforms the vacua to each other. So there are the tensor memory effects similar to the ones in general relativity, and the scalar memory effect, which is new. The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively.

Climbing up the memory staircase: Equatorial zoom-whirl orbits

The nonlinear, or null gravitational memory effect for zoom-whirl orbits around fast spinning Kerr black holes for extreme mass ratio systems has a staircase structure. The latter is characterized by a periodic fast increase in the memory during the whirl phases of the orbit, and near constant levels when the orbit is near apoapsis. We study the contribution of different spherical harmonic modes to this effect, and discuss the relative importance thereof. Because the hereditary memory effect increases in magnitude linearly in the number of periapsis passages on a dynamical time scale, while the oscillatory parent gravitational waves are sourced by an orbit that evolves on a much longer radiation reaction time scale, the magnitude of the former relative to the latter increases with time. We also consider orphan memory and the memory effect for extreme mass ratio inspirals. We then discuss the prospect of detection with the Laser Interferometer Space Antenna (LISA).

Gravitational waves affect vacuum entanglement

The entanglement harvesting protocol is an operational way to probe vacuum entanglement. This protocol relies on two atoms, modelled by Unruh-DeWitt detectors, that are initially unentangled. These atoms then interact locally with the field and become entangled. If the atoms remain spacelike separated, any entanglement between them is a result of entanglement that is `harvested' from the field. Thus, quantifying this entanglement serves as a proxy for how entangled the field is across the regions in which the atoms interacted. Using this protocol, it is demonstrated that while the transition probability of an individual inertial atom is unaffected by the presence of a gravitational wave, the entanglement harvested by two atoms depends sensitively on the frequency of the gravitational wave, exhibiting novel resonance effects when the energy gap of the detectors is tuned to the frequency of the gravitational wave. This suggests that the entanglement signature left by a gravitational wave may be useful in characterizing its properties, and potentially useful in exploring the gravitational-wave memory effect and gravitational-wave induced decoherence.

Coherent gravitational waveforms and memory from cosmic string loops

We construct, for the first time, the time-domain gravitational wave strain waveform from the collapse of a strongly gravitating Abelian Higgs cosmic string loop in full general relativity. We show that the strain exhibits a large memory effect during merger, ending with a burst and the characteristic ringdown as a black hole is formed. Furthermore, we investigate the waveform and energy emitted as a function of string width, loop radius and string tension Gμ. We find that the mass normalized gravitational wave energy displays a strong dependence on the inverse of the string tension E GW/M 0 ∝ 1/Gμ, with at the percent level, for the regime where Gμ ≳ 10−3. Conversely, we show that the efficiency is only weakly dependent on the initial string width and initial loop radii. Using these results, we argue that gravitational wave production is dominated by kinematical instead of geometrical considerations.

The soft mathcal{S} -matrix in gravity

The gravitational mathcal{S} -matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the gravitational memory effect is contained as an IR safe observable within the soft mathcal{S} -matrix.

Impulsive Signals and Gravitational Memory Effect

This paper is a review of the recently published article by Martin O’Loughlin and Hovhannes Demirchian [1] on covariant description of gravitational memory effect. There, a new approach was introduced to study geodesic congruences and their evolution after traversing impulsive signals, containing a mixture of material sources and gravitational waves. It was shown that the effect of the wave on the congruence is a discontinuity in the $$\mathcal{B}$$ -tensor of the congruence which provides a detector independent and covariant characterization of gravitational memory. It was also shown how different components of the impulsive signal effect the evolution of the congruence in the future.

A Multiple-Time-Scale Analog Circuit for the Compensation of Long-Term Memory Effects in GaN HEMT-Based Power Amplifiers

In this article, we present an analog circuit for the compensation of long-term memory effects in power amplifiers (PAs) based on GaN high-electron-mobility transistors (HEMTs). The analog compensation circuit (ACC) is supported on a charge-trapping behavioral model that features a state-dependent variable emission time constant, rather than a fixed emission time constant. This allows not only for the more accurate modeling and compensation of the nonlinear long-term memory effects experienced by GaN HEMT-based PAs, but also for the adaptation of the dynamics of the ACC to varying operating conditions, such as the ambient temperature. We demonstrate that the proposed ACC is able to successfully eliminate any multiple-time-constant transient symptom of current collapse following a high-power radio-frequency pulse or two-tone excitation and accurately preserve the class of operation of a GaN HEMT-based PA. Moreover, we also demonstrate that the proposed ACC can aid the linearization of GaN HEMT-based PAs for fifth-generation (5G) New Radio (NR) communications, allowing for the reduction in the complexity of the digital predistorter. For a 5G NR time-division duplexing signal with a bandwidth of 20 MHz, the inclusion of the ACC improved out-of-band emissions by over 15 dB and improved the error-vector magnitude by over 10 p.p. at essentially no cost to the PA’s power-added efficiency.

Einstein-Maxwell-dilaton theory in Newman-Penrose formalism

In this paper, we study the four-dimensional Einstein-Maxwell-dilaton theories in the Newman-Penrose (NP) formalism. We adapt the equations of motion into the NP formalism, and obtain the solution space that is asymptotic to the flat space-time. We then investigate the gravitational and electromagnetic memory effects. We find that the dilaton does not contribute to the displacement nor the kick memory effects, but it does contribute to the time-delayed memory effect.

Persistent Astrometric Deflections from Gravitational-Wave Memory.

Gravitational waves (GWs) produce small distortions in the observable distribution of stars in the sky. We describe the characteristic pattern of astrometric deflections created by a specific gravitational waveform called a burst with memory. Memory is a permanent, residual distortion of space left in the wake of GWs. We demonstrate that the astrometric effects of GW memory are qualitatively distinct from those of more broadly considered, oscillatory GWs-distinct in ways with potentially far-reaching observational implications. We discuss some such implications pertaining to the random-walk development of memory-induced deflection signatures over cosmological time spans and how those may influence observations of the cosmic microwave background.

Testing Brans-Dicke gravity with screening by scalar gravitational wave memory

The Brans-Dicke theory of gravity is one of the oldest ideas to extend general relativity by introducing a nonminimal coupling between the scalar field and gravity. The Solar System tests put tight constraints on the theory. In order to evade these constraints, various screening mechanisms have been proposed. These screening mechanisms allow the scalar field to couple to matter as strongly as gravity in low density environments while suppressing it in the Solar System. The Vainshtein mechanism, which is found in various modified gravity models such as massive gravity, braneworld models and scalar tensor theories, suppresses the scalar field efficiently in the vicinity of a massive object. This makes it difficult to test these theories from gravitational wave observations. We point out that the recently found scalar gravitational wave memory effect, which is caused by a permanent change in spacetime geometry due to the collapse of a star to a back hole can be significantly enhanced in the Brans-Dicke theory of gravity with the Vainshtein mechanism. This provides a possibility to detect scalar gravitational waves by a network of three or more gravitational wave detectors.

Gravitational-wave Memory from a Propagating Relativistic Jet: A Probe of the Interior of Gamma-Ray Burst Progenitors

Abstract It is believed that the relativistic jets of gamma-ray bursts (GRBs) should initially propagate through a heavy envelope of the massive progenitor stars or through merger ejecta formed from compact binary mergers. The interaction of a jet with a stellar envelope or merger ejecta can lead to the deceleration of the head material of the jet and simultaneously the formation of a hot cocoon. However, this jet-envelope/ejecta interaction is actually undetectable with electromagnetic radiation and can only be inferred indirectly by the structure of the breakout jet. Therefore, as a solution to this phenomenon, we suggest the jet-envelope/ejecta interaction can produce a gravitational-wave (GW) memory of an amplitude of , which could be detected with some future GW detectors sensitive in the frequency range from sub-Hertz to several tens of Hertz. This provides a potential direct way to probe the jet propagation and then the interior of the GRB progenitors.

Gravitational and electromagnetic memory

We present a unified investigation of memory effect in Einstein-Maxwell theory. We specify two types of memory effect, a velocity kick and a position displacement, by examining the motion of a single free falling charged test particle. Our result recovers the two known gravitational memory effect formulas and the two known electromagnetic memory effect formulas.

Persistent gravitational wave observables: Nonlinear plane wave spacetimes

In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of gravitational radiation. We defined three specific examples of persistent observables: a generalization of geodesic deviation that allowed for arbitrary acceleration, a holonomy observable involving a closed curve, and an observable that can be measured using a spinning test particle. For linearized plane waves, we showed that our observables could be determined just from one, two, and three time integrals of the Riemann tensor along a central worldline, when the observers follow geodesics. In this paper, we compute these three persistent observables in nonlinear plane wave spacetimes, and we find that the fully nonlinear observables contain effects that differ qualitatively from the effects present in the observables at linear order. Many parts of these observables can be determined from two functions, the transverse Jacobi propagators, and their derivatives (for geodesic observers). These functions, at linear order in the spacetime curvature, reduce to the one, two, and three time integrals of the Riemann tensor mentioned above.

Gravitational memory in the bulk

A method for detecting gravitational memory is proposed. It makes use of ingoing null geodesics instead of timelike geodesics in the original formulation by Christodoulou. It is argued that the method is applicable in the bulk of a spacetime. In addition, it is shown that BMS symmetry generators in Newman-Unti gauge have an interpretation in terms of the memory effect. This generalises the connection between BMS supertranslations and gravitational memory, discovered by Strominger and Zhiboedov at null infinity, to the bulk.

Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo

The detection of gravitational waves (GWs) from binary black holes (BBHs) has allowed the theory of general relativity to be tested in a previously unstudied regime: that of strong curvature and high GW luminosities. One distinctive and measurable effect associated with this aspect of the theory is the nonlinear GW memory effect. The GW memory effect is characterized by its effect on freely falling observers: the proper distance between their locations differs before and after a burst of GWs passes by their locations. Gravitational-wave interferometers, like the LIGO and Virgo detectors, can measure features of this effect from a single BBH merger, but previous work has shown that it will require an event that is significantly more massive and closer than any previously detected GW event. Finding evidence for the GW memory effect within the entire population of BBH mergers detected by LIGO and Virgo is more likely to occur sooner. A prior study has shown that the GW memory effect could be detected in a population of BBHs consisting of binaries like the first GW150914 event after roughly one-hundred events. In this paper, we compute forecasts of the time it will take the advanced LIGO and Virgo detectors (when the detectors are operating at their design sensitivities) to find evidence for the GW memory effect in a population of BBHs that is consistent with the measured population of events in the first two observing runs of the LIGO detectors. We find that after five years of data collected by the advanced LIGO and Virgo detectors the signal-to-noise ratio for the nonlinear GW memory effect in the population will be about three (near a previously used threshold for detection). We point out that the different approximation methods used to compute the GW memory effect can lead to notably different signal-to-noise ratios.