Braginsky and Thorne (1987) identified gravitational-wave 'bursts with memory' (BWMs) — transient signals whose strain settles to a permanent nonzero offset rather than returning to zero — as a fourth class of gravitational-wave signal, and posed the experimental problem of detecting them: which astrophysical sources produce detectable memory, which detectors achieve the required low-frequency sensitivity, and which search strategies extract the signal. The question survives in sharpened form. General relativity predicts both linear memory (from asymmetrically escaping masses and neutrinos, for example in core-collapse supernovae or high-velocity black-hole ejections) and the nonlinear Christodoulou memory carried by every gravitational-wave burst through the stress-energy of the waves themselves, yet as of 2026 every dedicated search — LIGO/Virgo/KAGRA catalog analyses through GWTC-5.0, both combined and hierarchical, and pulsar-timing-array searches by NANOGrav, PPTA and EPTA — reports no decisive evidence. The problem is to establish the first definitive observational evidence for gravitational-wave memory, whether from an individual event or by population-level inference over accumulated detections, with the physical source identified; published forecasts place decisive evidence from the current detector network at order 10310^3 cataloged mergers and routine individual-event detection with next-generation detectors.

Background

A gravitational-wave (GW) detector measures the strain hijTTh^{\mathrm{TT}}_{ij}: the dimensionless, transverse-traceless part of the metric perturbation, which in a laser interferometer appears as differential changes in the relative lengths of perpendicular arms. Experimenters conventionally sort expected signals into three classes — 'bursts' (the strain rises from zero, oscillates for a few cycles, and returns to zero), periodic waves, and stochastic backgrounds. Braginsky and Thorne (1987) emphasized a fourth class, the 'burst with memory' (BWM): the strain rises from zero, oscillates for a few cycles during a burst of duration Δt\Delta t, and then settles to a permanent nonzero value δhijTT\delta h^{\mathrm{TT}}_{ij} that persists after the wave has passed, so that freely falling test masses end up permanently displaced relative to one another.

Memory arises by two mechanisms. Linear memory is produced whenever masses or other forms of energy (notably neutrinos, which carry away most of the binding energy of a core-collapse supernova) escape an isolated system anisotropically, leaving a permanent change in the source's far field; the 1987 letter estimated memory strains of order 10−1810^{-18} only for strongly asymmetric Galactic supernovae, and comparable order-of-magnitude estimates for black holes ejected at high velocity by few-body interactions, making such sources detectable at best from within the local universe. Nonlinear memory, discovered by Christodoulou (1991) and called the Christodoulou effect, is produced by the stress-energy of the gravitational waves themselves: every GW burst, including the chirp of a compact-binary coalescence, carries it as a consequence of the nonlinear structure of general relativity, so it is a generic prediction rather than an exotic curiosity. The 1987 letter also established the basic search principle: for any detector, the optimal way to search for a BWM is to integrate the signal for a time τ^≃1/fopt\hat{\tau} \simeq 1/f_{\mathrm{opt}}, where foptf_{\mathrm{opt}} is the frequency at which the detector has its best amplitude sensitivity to ordinary one-cycle bursts; the sensitivity to a BWM of duration Δt⩽1/fopt\Delta t \leqslant 1/f_{\mathrm{opt}} then approximately equals the ordinary one-cycle burst sensitivity and is independent of Δt\Delta t. On this basis the letter computed limiting sensitivities for the detector concepts of its day: cryogenic resonant bars, Doppler tracking of spacecraft, pulsar timing, and ground- and space-based laser interferometry.

The experimental landscape has since been transformed. Since 2015 the LIGO (Laser Interferometer Gravitational-wave Observatory), Virgo and KAGRA ground-based interferometers routinely detect oscillatory signals from compact-binary coalescences (collected in the successive Gravitational-Wave Transient Catalogs, GWTC), but the nonlinear memory of a binary black hole merger is roughly an order of magnitude smaller in strain than its oscillatory parent signal, so it is individually below detection threshold and must be sought by stacking or hierarchical (population-level) inference over many events. Pulsar timing arrays (PTAs) — collaborations such as the Parkes Pulsar Timing Array (PPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) and the European Pulsar Timing Array (EPTA), which monitor millisecond pulsars — search the nanohertz band, where a memory burst would appear as a sudden, quadrupolar-patterned apparent change in pulse frequencies across the sky; the primary candidate sources are mergers of supermassive black hole binaries and hyperbolic encounters of such black holes. Space-based interferometry — the Laser Interferometer Space Antenna (LISA), at millihertz frequencies — targets the memory of massive black hole mergers. The standard analysis machinery is matched filtering (correlating data with template waveforms) with waveform models that include the memory contribution, Bayesian model comparison via Bayes factors (the odds of a memory hypothesis against a no-memory hypothesis), and hierarchical Bayesian inference, which combines many events while avoiding the prior-sensitivity pathologies of naively multiplying per-event Bayes factors. The astrophysical inputs that the 1987 letter flagged as uncertain — the fraction of core-collapse supernovae that eject mass and neutrinos asymmetrically enough to radiate detectable memory, and the occurrence rate of high-velocity black-hole ejections from few-body interactions — remain the rate-setting uncertainties for linear-memory forecasts, now informed by three-dimensional supernova simulations.

Problem Statement

The problem, in the form posed by Braginsky and Thorne (1987) and inherited by the modern literature, is to establish the first definitive observational evidence for a gravitational-wave burst with memory — a transient gravitational-wave signal whose transverse-traceless strain settles to a permanent nonzero offset δhijTT\delta h^{\mathrm{TT}}_{ij} after the burst — in data from any operating detector class (ground-based laser interferometers or pulsar timing arrays) or, in the next generation, from a space-based interferometer such as LISA, and to attribute the detected memory to its physical source class. The evidence sought may take one of two forms. (1) Single-event detection: a memory detection in an individual event — for example the neutrino- or ejecta-driven linear memory of a core-collapse supernova, or the memory of a supermassive-binary merger in pulsar timing data — at a level of statistical evidence recognized by the gravitational-wave community as a definitive detection, with the memory amplitude measured rather than assumed. (2) Population-level evidence: evidence for nonlinear memory in the accumulated catalog of compact-binary detections that constrains the memory contribution away from zero at a level recognized by the community as a definitive detection. In either form the memory is attributed to its physical source class and the astrophysical rate and amplitude implications are drawn, thereby closing the question the 1987 letter posed about whether the 'fourth class' of gravitational-wave signal is observable, from which sources, and by which search strategy. The empirical inputs are public: strain data for the LIGO/Virgo/KAGRA catalogs through GWTC-5.0 are released through the Gravitational-Wave Open Science Center, and the millisecond-pulsar timing data sets analyzed by NANOGrav, PPTA and EPTA are published alongside their searches; the events and sub-sets appropriate to the chosen route are selected from these data. By community convention, a definitive detection means a single-event memory measurement excluding zero at the conventional 5σ significance level, or a population-level cumulative ln BF ≥ 8 in favour of memory (the benchmark of Hübner et al. 2020, following Lasky et al. 2016). No published search meets this level of evidence — every dedicated search to date, including the hierarchical-inference constraint of Mitman, Isi and Farr (2026), remains consistent with zero memory. Upper limits on memory strain or source rates bound the question without resolving it. All physical forms of memory (nonlinear, or linear from anisotropic mass or neutrino ejection) and all detector classes qualify; no restriction to a particular source population, detector, or analysis method is intended.

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