We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS Collaboration's $\texttt{SpEC}$ code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using $\texttt{SpECTRE}$'s version of a Cauchy-characteristic extraction. We find that we can accurately resolve the strain's traditional $m=0$ memory modes and some of the $m\not=0$ oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Lastly, we find that signal-to-noise ratios of memory for LIGO, the Einstein Telescope (ET), and the Laser Interferometer Space Antenna (LISA) with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or Minimal Waveform models.
We describe neutrino radiation in general relativity by introducing the energy-momentum tensor of a null fluid into the Einstein equations. Investigating the geometry and analysis at null infinity, we prove that a component of the null fluid enlarges the Christodoulou memory effect of gravitational waves. The description of neutrinos in general relativity as a null fluid can be regarded as a limiting case of a more general description using the massless limit of the Einstein-Vlasov system. The present authors with co-authors have work in progress to generalize the results of this paper using t…
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 to deduce the property of the gravitational wave source. Quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory always use the energy flux of gravitational wave to calculate memory. Such relation between gravitational wave energy and memory has only been validated for post-Newtonian approximation. The result of numerical relativity about gravitational wave memory i…
General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or Christodoulou effect, which in a detector like LIGO or LISA shows as a permanent displacement of test masses and in radio telescopes like NANOGrav as a change in the frequency of pulsars' pulses. It was shown that electromagnetic fields and neutrino radiation enlarge the memory. Recently it has been understood that the two types of memory addressed in the literature…
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…
We study the displacement memory effect and its connection with the extended-BMS symmetries near the horizon of black holes. We show there is a permanent shift in the geodesic deviation vector relating two nearby timelike geodesics placed close to the horizon of black holes, upon the passage of gravitational waves. We also relate this memory effect with the asymptotic symmetries near the horizon of asymptotic black hole spacetimes. The shift of the relative position of the detectors is shown to be induced by a combination of BMS generators near the horizon. The displacement memory effect near …
We show how the Zel'dovich approximation and the second order displacement field of Lagrangian perturbation theory can be obtained from a general relativistic gradient expansion in ΛCDM cosmology. The displacement field arises as a result of a second order non-local coordinate transformation which brings the synchronous/comoving metric into a Newtonian form. We find that, with a small modification, the Zel'dovich approximation holds even on scales comparable to the horizon. The corresponding density perturbation is not related to the Newtonian potential via the usual Poisson equation but via a…
Detectability of Gravitational-Wave Memory with LISA: A Bayesian Approach
CEA（法国原子能和替代能源委员会）；Université Paris-Saclay（巴黎萨克雷大学）；Centre national d’études spatiales (CNES)（法国国家空间研究中心）；CERN（欧洲核子研究组织）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究院）；Niels Bohr Institute（尼尔斯·玻尔研究所）；KU Leuven（荷语鲁汶大学）；Leuven Gravity Institute（鲁汶引力研究所）；SISSA（国际高等研究院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
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…
Gravitational effect of "magnetic type" -- those having a curl-like character over large spheres -- are investigated, for isolated systems. The Bondi-Sachs-Newman-Penrose formalism clarifies a number of points, especially related to radiation memory. It is shown that the "memory tensor" is equivalent to the change in Bondi shear, from before to after the emission of radiation. This means that if magnetic radiation memory is present, at least one of the intervals bracketing the radiation must have non-zero magnetic shear but vanishing radiation. Such intervals, called here CPMS regimes, are sho…
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 val…
In this paper we demonstrate that a double Michelson interferometer with Fabry-Perot cavities in its arms is able to perform laser- and displacement-noise-free gravitational-wave (GW) detection if certain model assumptions are met. Assuming the input mirrors of a single Michelson/Fabry-Perot interferometer can be rigidly attached to beamsplitter on a central platform one can manipulate with interferometer's response signals in a way to cancel laser noise and displacement noise of all test masses except the cental platform. A pair of symmetrically positioned Michelson/Fabry-Perot interferometer…
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a permanent displacement of test masses in a laser interferometer gravitational wave detector. Christodoulou derived a precise formula for this permanent displacement in the Einstein vacuum (EV) case. We prove in Theorem 6 that for the EM equations this permanent displacement exhibits a…
We describe the irrotational dust component of the universe in terms of a relativistic gradient expansion and transform the resulting synchronous metric to a Newtonian coordinate system. The two metrics are connected via a space-like displacement field and a time-like perturbation, providing a relativistic generalization of the transformation from Lagrangian to Eulerian coordinates. The relativistic part of the displacement field generates already at initial time a non-local density perturbation at second order. This is a purely relativistic effect since it originates from space-time mixing. W…
Probing soft signals of gravitational-wave memory with space-based interferometers
School of Physics, Nanjing University（南京大学物理学院）；School of Frontier Sciences, Nanjing University（南京大学前沿科学中心）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences (UCAS)（中国科学院大学天文与空间科学学院）
Defining higher memory signals and forecasting their observation prospects for binary-black-hole mergers with next-generation gravitational-wave detectors
University of Virginia（弗吉尼亚大学）；University of Southampton（南安普顿大学）
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.
Niels Bohr Institute（尼尔斯·玻尔研究所）；CERN（欧洲核子研究中心）；KU Leuven（荷语鲁汶大学）；Universitat de València（瓦伦西亚大学）；Eberhard Karls University of Tübingen（蒂宾根大学）；Sofia University “St. Kliment Ohridski”（索菲亚大学）；Bulgarian Academy of Sciences（保加利亚科学院）
A simple estimate is given of gravitational wave memory for the inspiral and merger of a binary black hole system. Here the memory is proportional to the total energy radiated and has a simple angular dependence. This estimate might be helpful as a consistency check for numerical relativity memory waveforms.
The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent t…
Gravitational wave (GW) memory is an important prediction of general relativity. Existing works on the GW memory detection focus on the waveform analysis. It is hard for waveform analysis method to detect the GW memory due to its quasi-direct current behavior and weakness. We implement a completely different scheme in this work to estimate the GW memory. In this scheme, we firstly apply the Bondi-Metzner-Sachs method to calculate the GW memory of binary black hole based on numerical relativity simulation. Then we construct a surrogate model to relate binary black hole's parameters and the GW m…
We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether theorem, we construct new expressions for conserved currents and related superpotentials. They are covariant both under coordinate transformations and local Lorentz rotations, and allow us to construct well defined conserved charges, unlike earlier approaches. The advantage is achieved by an explicit presence of a displacement vector in the new expressions that c…
The conventional gravitational memory effect is a relative displacement in the position of two detectors induced by radiative energy flux. We find a new type of gravitational `spin memory' in which beams on clockwise and counterclockwise orbits acquire a relative delay induced by radiative angular momentum flux. It has recently been shown that the displacement memory formula is a Fourier transform in time of Weinberg's soft graviton theorem. Here we see that the spin memory formula is a Fourier transform in time of the recently-discovered subleading soft graviton theorem.
Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Albert Einstein Center, Institute for Theoretical Physics, University of Bern（伯尔尼大学阿尔伯特爱因斯坦中心理论物理研究所）
The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincaré vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this essay, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincaré…
Constraining superluminal Einstein-Æther gravity through gravitational memory
Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany（海德堡大学理论物理研究所）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy（帕多瓦大学伽利略·伽利雷物理与天文学系）；Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-Strasse 27, 8093, Zürich, Switzerland（苏黎世联邦理工学院理论物理研究所）；Center of Gravity, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark（哥本哈根大学尼尔斯·玻尔研究所引力中心）；Albert Einstein Center, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland（伯尔尼大学爱因斯坦中心理论物理研究所）
There exist gravitational memory effects in Brans-Dicke theory. They are closely related to the Bondi-Metzner-Sachs symmetries living 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 panetrating 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 d…
The gravitational wave memory effect is a prediction of general relativity. The presence of memory effect in gravitational wave signals not only provides the chance to test an important aspect of general relativity, but also represents a potentially non-negligible contribution to the waveform for certain gravitational wave events. In this paper, we study the prospect of detecting the gravitational wave memory effect directly with the planned space-based gravitational wave detector -- TianQin. We find that during its 5 years operation, for the gravitational wave signals that could be detected b…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by an extremely complex set of coupled, nonlinear, hyperbolic-elliptic partial differential equations. The largest parallel supercomputers are finally approaching the speed and memory required to solve the complete set of Einstein's equations for the first time since they were written over 80 years ago, allowing one to attempt full 3D simulations of such excit…
We investigate the gravitational memory effect for linearized perturbations off of Minkowski space in odd spacetime dimensions $d$ by examining the effects of gravitational radiation from classical point particle scattering. We also investigate analogous memory effects for electromagnetic and scalar radiation. We find that there is no gravitational memory effect in all odd dimensions. For scalar and electromagnetic fields, there is no memory effect for $d\geq 7$; for $d=3$ there is an infinite momentum memory effect, whereas for $d=5$ there is no momentum memory effect but the displacement of …
The non-linear gravitational-wave memory effect is a prediction of general relativity in which test masses are permanently displaced by gravitational radiation. We implement a method for calculating the expected memory waveform from an oscillatory gravitational-wave time series. We use this method to explore the phenomenology of gravitational-wave memory using a numerical relativity surrogate model. Previous methods of calculating the memory have considered only the dominant oscillatory ($\ell=2$, $m=|2|$) mode in the spherical harmonic decomposition or the post-Newtonian expansion. We explore…
We compute the non-linear memory contributions to the gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian (3PN) order in general relativity. These contributions are hereditary in nature as they are sourced by gravitational waves emitted during the binary's entire dynamical past. Combining these with already available instantaneous and tail contributions we get the complete 3PN accurate gravitational waveform.
Gravitational Memory from Hairy Binary Black Hole Mergers
CERN（欧洲核子研究组织）；KU Leuven（荷语鲁汶大学）；Universitat de València（瓦伦西亚大学）；Eberhard Karls University of Tübingen（蒂宾根大学）；Sofia University “St. Kliment Ohridski”（索非亚大学）；Bulgarian Academy of Sciences（保加利亚科学院）
In GW150914, approximately $3M_{\odot}$ were radiated away as gravitational waves from the binary black hole system as it merged. The stress energy of the gravitational wave itself causes a nonlinear memory effect in the detectors here on Earth called the Christodoulou memory. We use an approximation that can be applied to numerical relativity waveforms to give an estimate of the displacement magnitude and the profile of the nonlinear memory. We give a signal to noise ratio for a single GW150914-like detection event, and by varying the total mass and distance parameters of the event, we find d…
