The NANOGrav 12.5 yr Data Set: Search for Gravitational Wave Memory

We present the results of a search for nonlinear gravitational-wave (GW) memory in the NANOGrav 15 yr data set. We find no significant evidence for memory signals in the data set, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential GW memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5 and 15 yr NANOGrav data sets.

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.

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.

This article reviews one of the most intriguing properties of black hole spacetimes known in the literature -- gravitational memory effect, and its connection with asymptotic symmetries, also termed as Bondi-van der Burg-Metzner-Sachs (BMS) symmetries, emerging near the horizon of black holes. Gravitational memory is a non-oscillatory part of the gravitational wave amplitude which generates a permanent displacement for freely falling test particles or test detectors. We highlight a model scenario where asymptotic symmetries appear as a soldering freedom in the context of stitching of two black hole spacetimes, and examine the impact of the interaction between test detectors and horizon shells. Further, we provide a more realistic approach of computing displacement memory for near-horizon asymptotic symmetries which is analogous to the conventional memory originally obtained at asymptotic null infinity.

Gravitational-wave memory is a non-linear effect predicted by general relativity that remains undetected. We apply a Bayesian analysis framework to search for gravitational-wave memory using binary black hole mergers in LIGO-Virgo-KAGRA’s third gravitational-wave transient catalogue. We obtain a Bayes factor of ln⁡BF=0.01 , in favour of the no-memory hypothesis, which implies that we are unable to measure memory with currently available data. This is consistent with previous work, suggesting that a catalogue of O(2000) binary black hole mergers is needed to detect memory. We look for new physics by allowing the memory amplitude to deviate from the prediction of general relativity by a multiplicative factor A. We obtain an upper limit of A < 23 (95% credibility).

The nonlinear memory effect is a slowly growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite this fact, the nonlinear memory is not easily extracted from current numerical relativity simulations. After reviewing the linear and nonlinear memory I summarize some recent work, including (1) computations of the memory contribution to the inspiral waveform amplitude (thus completing the waveform to third post-Newtonian order); (2) the first calculations of the nonlinear memory that include all phases of binary black hole coalescence (inspiral, merger, ringdown); and (3) realistic estimates of the detectability of the memory with LISA.

&lt;p&gt;&lt;strong&gt;The future of theoretical physics is unclear. Two large areas that fall under the umbrella of theoretical physics are cosmology and quantum gravity. Modern cosmology is relatively a much younger field than quantum gravity, and both of these fields require further developments of general relativity. In this thesis we do not hope to resolve the problems facing modern cosmology or theories of quantum gravity. Rather, we will conduct original research into aspects of general relativity that may be used in the future to aid the development and testing of theories of cosmology and quantum gravity.&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;It is our view that the largest problem facing astrophysics and cosmology stem from the existence of the dark sector of the Universe. The implication here being that more than ninety percent of the energy density of the Universe is “missing in action” and seemingly consists of dark energy and dark matter. Furthermore, it is apparent that there exist conceptual flaws in our understanding of observational concepts such as expansion versus motion and observer biases. To this end, we investigate the standard spacetime metric used in cosmology, the Friedmann–Lemaˆıtre-Roberston–Walker (FLRW) metric in a peculiar coordinate system — the Painlev´e–Gullstrand coordinates. In this coordinate system (slicing), space is no longer expanding, rather, the galaxies are receding from each other. We hope this will aid in the understanding of expansion, motion, curvature, and observer bias with future work. We further investigate the possibility of black holes in cosmology being directly coupled to the accelerated expansion of the Universe — in other words, black holes as a source for dark energy. However, we show that this is highly implausible.&lt;/p&gt;&lt;p&gt;Relatively recently it has been postulated that the near black hole horizon limit may be a regime where quantum gravity effects become relevant i.e., quantum gravity may not be restricted to near the Planck scale. We investigate a curious model of black and white holes that shows how one may transition into the other over a finite period of time. This is research conducted in the near horizon limit of the Schwarzschild black hole. We introduce a time dependent function into the usual Schwarzschild black hole spacetime (leaving this new spacetime not a simple coordinate transformed version of the original). This function allows the black hole to transition into a white hole. Importantly, the action for this transition can be shown to be zero, meaning it can be added to the Feynman path integral at no cost.&lt;/p&gt;&lt;p&gt;Finally, we move to investigating the black hole memory effect. During the last decade, there has been an interesting connection made between the Bondi– Metzner–Sachs (BMS) group — an infinite dimensional group of symmetries found at null infinity — and the gravitational memory effect. In particular, it was shown that the passage of a gravitational wave that alters a Schwarzschild black hole is seen as a supertranslation of the spacetime at null infinity. We extend these calculations to the Kerr and Kerr–Newman black holes. Hence, showing that there may be a way to verify the abstract mathematical ideas predicated on the BMS group by detection of the memory effect in future observations.&lt;/p&gt;&lt;p&gt;It is our hope that when future gravitational wave detectors such as the laser-interferometer-space-antenna (LISA) are launched, research conducted in this thesis may shed light on how the memory may relate to black holes in their asymptotic &amp; near horizon limits to aid our understanding of the nature of quantum gravity.&lt;/p&gt;

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.

We describe an experiment to measure the electromagnetic analog of gravitational wave memory, the so-called electromagnetic (EM) memory. Whereas gravitational wave memory is a residual displacement of test masses, EM memory is a residual velocity (i.e. kick) of test charges. The source of gravitational wave memory is energy that is not confined to any bounded spatial region: in the case of binary black hole mergers the emitted energy of gravitational radiation as well as the recoil energy of the final black hole. Similarly, EM memory requires a source whose charges are not confined to any bounded spatial region. While particle beams can provide unbounded charges, their currents are too small to be practical for such an experiment. Instead we propose a short microwave pulse applied to the center of a long dipole antenna. In this way the measurement of the kick can be done quickly enough that the finite size of the antenna does not come into play and it acts for our purposes the same as if it were an infinite antenna.

Known entropy bounds, and the Generalized Second Law, were recently shown to imply bounds on the information arriving at future null infinity. We complete this derivation by including the contribution from gravitons. We test the bounds in classical settings with gravity and no matter. In Minkowski space, the bounds vanish on any subregion of the future boundary, independently of coordinate choices. More generally, the bounds vanish in regions where no gravitational radiation arrives. In regions that do contain Bondi news, the bounds are compatible with the presence of information, including the information stored in gravitational memory. All of our results are consistent with the equivalence principle, which states that empty Riemann-flat spacetime regions contain no classical information. We also discuss the possibility that Minkowski space has an infinite vacuum degeneracy labeled by a choice of Bondi coordinates (a classical parameter, if physical). We argue that this degeneracy cannot have any observational consequences if the equivalence principle holds. Our bounds are consistent with this conclusion.

The gravitational memory effect manifests gravitational nonlinearity, degenerate vacua, and asymptotic symmetries; its detection is considered challenging. We propose using a space-borne interferometer to detect memory signals from stellar-mass binary black holes (BBHs), typically targeted by ground-based detectors. We use DECIGO detector as an example. Over 5 years, DECIGO is estimated to detect approximately 2,036 memory signals (SNRs &gt; 3) from stellar-mass BBHs. Simulations used frequency-domain memory waveforms for direct SNR estimation. Predictions utilized a GWTC-3 constrained BBH population model (Power law + Peak mass, DEFAULT spin, Madau–Dickinson merger rate). The analysis used conservative lower merger rate limits and considered orbital eccentricity. The high detection rate stems from strong memory signals within DECIGO’s bandwidth and the abundance of stellar-mass BBHs. This substantial and conservative detection count enables statistical use of the memory effect for fundamental physics and astrophysics. DECIGO exemplifies that space interferometers may better detect memory signals from smaller mass binaries than their typical targets. Detectors in lower frequency bands are expected to find strong memory signals from ∼104 M ⊙ binaries.

We define a procedure by which observers can measure a type of special-relativistic linear and angular momentum $(P^a, J^{ab})$ at a point in a curved spacetime using only the spacetime geometry in a neighborhood of that point. The method is chosen to yield the conventional results in stationary spacetimes near future null infinity. We also explore the extent to which spatially separated observers can compare the values of angular momentum that they measure and find consistent results. We define a generalization of parallel transport along curves which gives a prescription for transporting values of angular momentum along curves that yields the correct result in special relativity. If observers use this prescription, then they will find that the angular momenta they measure are observer dependent, because of the effects of spacetime curvature. The observer dependence can be quantified by a kind of generalized holonomy. We show that bursts of gravitational waves with memory generically give rise to a nontrivial generalized holonomy: there is, in this context, a close relation between the observer dependence of angular momentum and the gravitational-wave memory effect.

We show that charges associated with the internal Lorentz symmetries of general relativity, with higher derivative boundary terms included in the action, capture observable gravitational wave effects. In particular, the Gauss-Bonnet charge measures the precession rate of a freely-falling gyroscope, while the Pontryagin charge encodes the relative radial acceleration of freely-falling test masses. This relation highlights the importance of the tetrad formalism and the physical significance of asymptotic internal Lorentz symmetries.

We propose an upgrade to Advanced LIGO (aLIGO), named LIGO-LF, that focuses on improving the sensitivity in the 5-30Hz low-frequency band, and we explore the upgrade's astrophysical applications. We present a comprehensive study of the detector's technical noises and show that with technologies currently under development, such as interferometrically sensed seismometers and balanced-homodyne readout, LIGO-LF can reach the fundamental limits set by quantum and thermal noises down to 5Hz. These technologies are also directly applicable to the future generation of detectors. We go on to consider this upgrade's implications for the astrophysical output of an aLIGO-like detector. A single LIGO-LF can detect mergers of stellar-mass black holes (BHs) out to a redshift of z≃6 and would be sensitive to intermediate-mass black holes up to 2000 M_{⊙}. The detection rate of merging BHs will increase by a factor of 18 compared to aLIGO. Additionally, for a given source the chirp mass and total mass can be constrained 2 times better than aLIGO and the effective spin 3-5 times better than aLIGO. Furthermore, LIGO-LF enables the localization of coalescing binary neutron stars with an uncertainty solid angle 10 times smaller than that of aLIGO at 30Hz and 4 times smaller when the entire signal is used. LIGO-LF also significantly enhances the probability of detecting other astrophysical phenomena including the tidal excitation of neutron star r modes and the gravitational memory effects.

Observations indicate that nearly all galaxies contain supermassive black holes at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays. We have searched the North American Nanohertz Observatory for Gravitational Waves 11 yr data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95% upper limits on the strength of GWs from such sources. At = 8 nHz, we placed a sky-averaged upper limit of h 0 &lt; 7.3(3) × 10−15. We also developed a technique to determine the significance of a particular signal in each pulsar using “dropout” parameters as a way of identifying spurious signals. From these upper limits, we ruled out SMBHBs emitting GWs with = 8 nHz within 120 Mpc for , and within 5.5 Gpc for at our most sensitive sky location. We also determined that there are no SMBHBs with emitting GWs with = 2.8–317.8 nHz in the Virgo Cluster. Finally, we compared our strain upper limits to simulated populations of SMBHBs, based on galaxies in the Two Micron All-Sky Survey and merger rates from the Illustris cosmological simulation project, and found that only 34 out of 75,000 realizations of the local universe contained a detectable source.