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Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

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Physical Review D 2025年第10期111卷 104042-104042页

作者： Uddeepta Deka Gopalkrishna Prabhu Md Arif Shaikh Shasvath J. Kapadia Vijay Varma Scott E. Field International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune 411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya (affiliated to Vidyasagar University) Manikpara 721513 West Bengal India Department of Physics and Astronomy Seoul National University Seoul 08826 South Korea Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor F˜(t). We show this by constructing F˜(t) for two lens models, viz. point-mass lens, and singular isothermal sphere, which notably includes logarithmic divergence behavior. We find both surrogates reproduce the original lens models accurately, with mismatches ≲5×10−4 across a range of plausible microlensed binary black hole sources observed by the Einstein Telescope. This surrogate is between 5 and 103 times faster than the underlying lensing models, and can be evaluated in about 100 ms. The accuracy and efficiency attained by our surrogate models will enable practical parameter estimation analyses of microlensed GWs.

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High-Precision Ringdown Surrogate Model for Non-Precessing Binary Black Holes

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arXiv 2024年

作者： Zertuche, Lorena Magaña Stein, Leo C. Mitman, Keefe Field, Scott E. Varma, Vijay Boyle, Michael Deppe, Nils Kidder, Lawrence E. Moxon, Jordan Pfeiffer, Harald P. Scheel, Mark A. Nelli, Kyle C. Throwe, William Vu, Nils L. Department of Physics and Astronomy University of Mississippi UniversityMS38677 United States Theoretical Astrophysics 350-17 California Institute of Technology PasadenaCA91125 United States Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research East Hall University of Rhode Island KingstonRI02881 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Laboratory for Elementary Particle Physics Cornell University IthacaNY14853 United States Department of Physics Cornell University IthacaNY14853 United States Am Mühlenberg 1 Potsdam14476 Germany

Highly precise and robust waveform models are required as improvements in detector sensitivity enable us to test general relativity with more precision than ever before. In this work, we introduce a spin-aligned surrogate ringdown model. This ringdown surrogate, NRSur3dq8_RD, is built with numerical waveforms produced using Cauchy-characteristic evolution. In addition, these waveforms are in the superrest frame of the remnant black hole allowing us to do a correct analysis of the ringdown spectrum. The novel prediction of our surrogate model is complex-valued quasinormal mode (QNM) amplitudes, with median relative errors of 10−2 − 10−3 over the parameter space. Like previous remnant surrogates, we also predict the remnant black hole’s mass and spin. The QNM mode amplitude errors translate into median errors on ringdown waveforms of ∼ 10−4. The high accuracy and QNM mode content provided by our surrogate will enable high-precision ringdown analyses such as tests of general relativity. Our ringdown model is publicly available through the python package surfinBH. Copyright © 2024, The Authors. All rights reserved.

关键词： Relativity

Learning orbital dynamics of binary black hole systems from gravitational wave measurements

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Physical Review research 2021年第4期3卷 043101-043101页

作者： Brendan Keith Akshay Khadse Scott E. Field Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and noneccentric orbits. We show that the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a data-driven approach to studying the dynamics of binary black hole systems.

关键词： General relativity equations & solutions Gravitational waves

Aretakis Hair for Extreme Kerr Black Holes with Axisymmetric Scalar Perturbations

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arXiv 2023年

作者： Burko, Lior M. Khanna, Gaurav Sabharwal, Subir Theiss Research La Jolla CA92037 United States Department of Physics University of Rhode Island KingstonRI02881 United States Center for Computational Research University of Rhode Island KingstonRI02881 United States Physics Department Center for Scientific Computing & Data Science Research University of Massachusetts Dartmouth DartmouthMA02747 United States

We study the evolution of axially-symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments ′ higher than the least radiative mode, and we measure modes - and for the first time also horizon charges - that are excited by mode coupling interactions. We then find the Ori-Sela prefactors, a certain quantity that can be evaluated at finite distances and the Aretakis constant along the event horizon of the extreme Kerr black hole for a sequence of initial data preparations that differ only by their distance from the event horizon. We find that for initial data in the near field there is a linear relationship of the Aretakis constant and the Ori-Sela prefactor. For initial data farther than these the linear relationship is not universal, and we propose that stronger numerical simulations would be needed to regain linearity. The linear relationship suggests that the Aretakis charge along the event horizon can be measured at a finite distance, thereby extending this type of violation of the no-hair theorems from the least radiative axisymmetric mode also to situations that involve mode coupling. © 2023, CC BY.

关键词： Stars

Superconvergent Discontinuous Galerkin Method for the Scalar Teukolsky Equation on Hyperboloidal Domains: Efficient Waveform and Self-Force Computation

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arXiv 2025年

作者： Vishal, Manas Field, Scott E. Gottlieb, Sigal Ryan, Jennifer Department of Mathematics University of Massachusetts DartmouthMA02747 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta distribution) for self-force computations. Spectrally accurate methods, such as nodal discontinuous Galerkin (DG) methods, are well suited for these tasks. Their numerical errors typically decrease as ∝ (∆x)N+1, where ∆x is the subdomain size and N is the polynomial degree of the approximation. However, certain DG schemes exhibit superconvergence, where truncation, phase, and dispersion errors can decrease as fast as ∝ (∆x)2N+1. Superconvergent numerical solvers are, by construction, extremely efficient and accurate. We theoretically demonstrate that our DG scheme for the scalar Teukolsky equation with a distributional source is superconvergent, and this property is retained when combined with the hyperboloidal layer compactification technique. This ensures that waveforms, total energy and angular-momentum fluxes, and self-force computations benefit from superconvergence. We empirically verify this behavior across a family of hyperboloidal layer compactifications with varying degrees of smoothness. Additionally, we show that self-force quantities for circular orbits, computed at the point particle’s location, also exhibit a certain degree of superconvergence. Our results underscore the potential benefits of numerical superconvergence for efficient and accurate gravitational waveform simulations based on DG methods. Copyright © 2025, The Authors. All rights reserved.

关键词： Galerkin methods

Scalar and gravitational transient hair for near-extremal black holes

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Physical Review D 2022年第4期105卷 044032-044032页

作者： Kevin González-Quesada Subir Sabharwal Gaurav Khanna Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Data Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics University of Rhode Island Kingston Rhode Island 02881 USA

We study the existence and nature of Aretakis charge and its potentially observable imprint at a finite distance from the horizon (Ori coefficient) in near-extremal black hole backgrounds. Specifically, we consider the time evolution of horizon penetrating scalar and gravitational perturbations with compact support on near-extremal Reissner-Nordström and Kerr. We do this by numerically solving the Teukolsky equation and determining the Aretakis charge values on the horizon and at a finite distance from the black hole. We demonstrate that these values are no longer strictly conserved in the nonextremal case; however, their decay rate can be arbitrarily slow as the black hole approaches extremality allowing for the possibility of their observation as a transient hair.

关键词： Classical black holes General relativity Gravitational wave sources Gravitational waves Numerical relativity

Comparing numerical relativity and perturbation theory waveforms for a non-spinning equal-mass binary

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arXiv 2023年

作者： Islam, Tousif Field, Scott E. Khanna, Gaurav Department of Mathematics University of Massachusetts DartmouthMA02747 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States

Past studies have empirically demonstrated a surprising agreement between gravitational waveforms computed using adiabatic-driven-inspiral point-particle black hole perturbation theory (ppBHPT) and numerical relativity (NR) following a straightforward calibration step, sometimes referred to as α-β scaling. Specifically focusing on the quadrupole mode, this calibration technique necessitates only two time-independent parameters to scale the overall amplitude and time coordinate. In this article, part of a special issue, we investigate this scaling for non-spinning binaries at the equal mass limit. Even without calibration, NR and ppBHPT waveforms exhibit an unexpected degree of similarity after accounting for different mass scale definitions. Post-calibration, good agreement between ppBHPT and NR waveforms extends nearly up to the point of the merger. We also assess the breakdown of the time-independent assumption of the scaling parameters, shedding light on current limitations and suggesting potential generalizations for the α-β scaling technique. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

On the approximate relation between black-hole perturbation theory and numerical relativity

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arXiv 2023年

作者： Islam, Tousif Khanna, Gaurav Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States

We investigate the interplay between numerical relativity (NR) and adiabatic point-particle black hole perturbation theory (ppBHPT) in the comparable mass regime for quasi-circular non-spinning binary black holes. Specifically, we reassess the α-β scaling technique, previously introduced by Islam et al. [1], as a means to effectively match ppBHPT waveforms to NR waveforms within this regime. In particular, α rescales the amplitude and β rescales the time (and hence the phase). Utilizing publicly available long NR data (SXS:BBH:2265 [2]) for a mass ratio of 1: 3, encompassing the final ∼ 65 orbital cycles of the binary evolution, we examine the range of applicability of such scalings. We observe that the scaling technique remains effective even during the earlier stages of the inspiral. Additionally, we provide commentary on the temporal evolution of the α and β parameters and discuss whether they can be approximated as constant values. Consequently, we derive the α-β scaling as a function of orbital frequencies and demonstrate that it is equivalent to a frequency-dependent correction. We further provide a brief comparison between post-Newtonian (PN) waveforms and the rescaled ppBHPT waveform at a mass ratio of 1: 3 and comment on their regime of validity. Finally, we explore the possibility of using PN theory to obtain the α-β calibration parameters and still provide a rescaled ppBHPT waveform that matches NR. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

Exact block encoding of imaginary time evolution with universal quantum neural networks

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Physical Review research 2025年第1期7卷 013306-013306页

作者： Ermal Rrapaj Evan Rule National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA RIKEN iTHEMS Wako Saitama 351-0198 Japan Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function Ansatz is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the Ansatz yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

关键词： Stochastic systems