arXiv subjects

Gaurav Khanna

Publications and source records attributed to Gaurav Khanna.

At least 37 records · Page 2Linked to original sources

arXiv2024

Gravitational waves from black hole emission

Using adiabatic point-particle black hole perturbation theory, we simulate plausible gravitational wave~(GW) signatures in two exotic scenarios (i) where a small black hole is emitted by a larger one ('black hole emission') and (ii) where a small black hole is emitted by a larger one and subsequently absorbed back ('black hole absorption'). While such scenarios are forbidden in general relativity!(GR), alternative theories (such as certain quantum gravity scenarios obeying the weak gravity conjecture, white holes, and Hawking radiation) may allow them. By leveraging the phenomenology of black hole emission and absorption signals, we introduce straightforward modifications to existing gravitational waveform models to mimic gravitational radiation associated with these exotic events. We anticipate that these (incomplete but) initial simulations, coupled with the adjusted waveform models, will aid in the development of null tests for GR using GWs.

gr-qc↗

arXiv2024

Angular Momentum for Black Hole Binaries in Numerical Relativity

The extensive catalog of waveforms, with details of binary black hole inspiral and merger, offer an opportunity to understand black hole interactions beyond the large separation regime. We envision a research program that focuses on the transfer of angular momentum from spin of the individual holes to the orbital angular momentum and the role of tidal coupling in the process. That analysis will require the formulation of an expression for the orbital angular momentum of a binary, an expression that is useful at small separations, since that regime is well out of the range of Newtonian approximations and is where tidal coupling should be most interesting. We report here such an expression, a binary orbital angular momentum based on numerical relativity results for quasi-circular orbits, that agrees remarkably well with a similar quantity constructed with particle-perturbation techniques for the Kerr geometry.

gr-qc↗

arXiv2024

Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by "stitching" together a long inspiral waveform from a sequence of waveform snapshots, each of which corresponds to a particular geodesic orbit. We show that the complicated total waveform can be regarded as a sum of "voices." Each voice evolves in a simple way on long timescales, a property which can be exploited to efficiently produce waveform models that faithfully encode the properties of EMRI systems. We look at examples for a range of different orbital geometries: spherical orbits, equatorial eccentric orbits, and one example of generic (inclined and eccentric) orbits. To our knowledge, this is the first calculation of a generic EMRI waveform that uses strong-field radiation reaction. We examine waveforms in both the time and frequency domains. Although EMRIs evolve slowly enough that the stationary phase approximation (SPA) to the Fourier transform is valid, the SPA calculation must be done to higher order for some voices, since their instantaneous frequency can change from chirping forward ($\dot f > 0$) to chirping backward ($\dot f < 0$). The approach we develop can eventually be extended to more complete EMRI waveform models, for example to include effects neglected by the adiabatic approximation such as the conservative self force and spin-curvature coupling.

gr-qc↗

arXiv2024

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

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.

gr-qc↗

arXiv2024

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

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, 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 (\texttt{SXS:BBH:2265}~\cite{sxs_collaboration_2019}) for a mass ratio of $1:3$, encompassing the final $\sim 65$ 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 $q=3$ 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.

gr-qc↗

arXiv2023

Binary Black Hole Coalescence Phenomenology from Numerical Relativity

The major source of ground-based gravitational wave detectors, the inspiral and merger of comparable mass binary black holes (BBH), consists of a slow quasicircular inspiral, a merger to form a single remnant hole, and the quasinormal ringing of that remnant. The first and last of these epochs are amenable to well developed and familiar approximations: Newtonian or post-Newtonian for the first, and BH perturbation methods for the last. Ironically, the middle epoch, the merger, generates most of the GW emission, yet has been accessible so far only to numerical relativity. Here we add the close-limit approximation for the phenomenology of the merger. With the completed set of methods (Newtonian/post-Newtonian; close limit; BH perturbation theory) we show that not only can we understand the results of BBH coalescence, but - with reasonable accuracy - we can {\it predict} the resulting radiation and remnant.

gr-qc↗

arXiv2023

Interplay between numerical relativity and perturbation theory : finite size effects

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) in the comparable mass ratio regime. In the ppBHPT framework, the secondary black hole is treated as a point particle, neglecting its finite size. Our study focuses on addressing the missing finite size effect in the ppBHPT framework and proposing a method for incorporating the size of the secondary into the perturbation theory framework. We demonstrate that by considering the secondary as a finite size object, the BHPT waveforms closely match NR waveforms. Additionally, we revisit the $α$-$β$ scaling technique, which was previously introduced by Islam et al, as a means to effectively match ppBHPT waveforms to NR waveforms. We further analyze the scaling procedure and decompose it into different components, attributing them to various effects, including the corrections arising from the finite size of the secondary black hole.

gr-qc↗

arXiv2023

Survey of gravitational wave memory in intermediate mass ratio binaries

The non-linear gravitational wave (GW) memory effect is a distinct prediction in general relativity. While the effect has been well studied for comparable mass binaries, it has mostly been overlooked for intermediate mass ratio inspirals (IMRIs). We offer a comprehensive analysis of the phenomenology and detectability of memory effects, including contributions from subdominant harmonic modes, in heavy IMRIs consisting of a stellar mass black hole and an intermediate mass black hole. When formed through hierarchical mergers, for example when a GW190521-like remnant captures a stellar mass black hole, IMRI systems have a large total mass, large spin on the primary, and possibly residual eccentricity; features that potentially raise the prospect for memory detection. We compute both the displacement and spin non-linear GW memory from the $m \neq 0$ gravitational waveforms computed within a black hole perturbation theory framework that is partially calibrated to numerical relativity waveforms. We probe the dependence of memory effects on mass ratio, spin, and eccentricity and consider the detectability of a memory signal from IMRIs using current and future GW detectors. We find that (i) while eccentricity introduces additional features in both displacement and spin memory, it does not appreciatively change the prospects of detectability, (ii) including higher modes into the memory computation can increase singal-to-noise (SNR) values by about 7\% in some cases, (iii) the SNR from displacement memory dramatically increases as the spin approaches large, positive values, (iv) spin memory from heavy IMRIs would, however, be difficult to detect with future generation detectors even from highly spinning systems. Our results suggest that hierarchical binary black hole mergers may be a promising source for detecting memory and could favorably impact memory forecasts.

gr-qc↗

arXiv2023

Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution

Linear wave equations sourced by a Dirac delta distribution $δ(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with source terms proportional to $\partial^n δ/\partial x^n$. Despite the presence of singular source terms, which imply discontinuous or potentially singular solutions, our DG method achieves global spectral accuracy even at the source's location. Our DG method is developed for the wave equation written in fully first-order form. The first-order reduction is carried out using a distributional auxiliary variable that removes some of the source term's singular behavior. While this is helpful numerically, it gives rise to a distributional constraint. We show that a time-independent spurious solution can develop if the initial constraint violation is proportional to $δ(x)$. Numerical experiments verify this behavior and our scheme's convergence properties by comparing against exact solutions.

math.NA↗

arXiv2023

Aretakis Hair for Extreme Kerr Black Holes with Axisymmetric Scalar Perturbations

We study the evolution of axially-symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments $\ell^{\prime}$ higher than the least radiative mode, and we measure modes $\ell$ -- 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.

gr-qc↗

arXiv2023

Remnant black hole properties from numerical-relativity-informed perturbation theory and implications for waveform modelling

During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to compute the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational radiation. Using this package, we compute the remnant properties of the final black hole in case of non-spinning BBH mergers with mass ratios ranging from q=2.5 to q=1000 using waveform modes generated from BHPTNRSur1dq1e4, a recently developed numerical-relativity-informed surrogate model based on black-hole perturbation theory framework. We validate our results against the remnant properties estimated from numerical relativity (NR) surrogate models in the comparable mass ratio regime and against recently available high-mass-ratio NR simulations at q=[15,32,64]. We find that our remnant property estimates computed from fluxes at future null infinity closely match the estimates obtained from the NR surrogate model of apparent horizon data. Using Gaussian process regression fitting methods, we train a surrogate model, {BHPTNR_Remnant, for the properties of the remnant black hole arising from BBH mergers with mass ratios from q=2.5 to q=1000. Finally, we discuss potential improvements in the BHPTNRSur1dq1e4 waveform model when including remnant information. We make both the gw_remnant and BHPTNR_Remnant packages publicly available.

gr-qc↗

arXiv2022

Issues in the comparison of particle perturbations and numerical relativity for binary black hole mergers

Recent work on improved efficiency of calculations for extreme mass ratio inspirals has produced the useful byproduct of comparisons of inspirals of comparable mass by particle perturbation (PP) methods and by numerical relativty (NR). Here we point out: (1) In choosing the rescaling of the masses, consideration must be given to the differences in the PP and NR methods even in the earliest, least nonlinear regime; in particular barycenter effects must be addressed. (2) Care must be given to the comparison of the nonspinning remnant in PP and the rapidly spinning remnant in NR.

gr-qc↗

arXiv2022

Measuring quasi-normal mode amplitudes with misaligned binary black hole ringdowns

In recent work, we examined how different modes in the ringdown phase of a binary coalescence are excited as a function of the final plunge geometry. At least in the large mass ratio limit, we found a clean mapping between angles describing the plunge and the amplitude of different quasi-normal modes (QNMs) which constitute the ringdown. In this study, we use that mapping to construct a waveform model expressed as a sum of QNMs where the mode amplitudes and phases are determined by the source plunge parameters. We first generate a large number of calibration waveforms and interpolate between fits of each mode amplitude and phase up to $\ell \leq 8$ and $\ell - |m| \leq 4$. The density of our calibration data allows us to resolve important features such as phase transition discontinuities at large misalignments. Using our ringdown waveform model, we then perform Bayesian parameter estimation with added white Gaussian noise to demonstrate that, in principle, the mode amplitudes can be measured and used to constrain the plunge geometry. We find that inferences are substantially improved by incorporating prior information constraining mode excitation, which motivates work to understand and characterize how the QNM excitation depends on the coalescence geometry. These results are part of a broader effort to map the mode excitation from arbitrary masses and spins, which will be useful for characterizing ringdown waves in upcoming gravitational-wave measurements.

gr-qc↗

arXiv2022

Surrogate model for gravitational wave signals from non-spinning, comparable- to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes several more spherical harmonic modes up to $\ell=10$, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as $2.5$, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from $15$ to $32$, and find the dominant quadrupolar modes agree to better than $\approx 10^{-3}$. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors.

gr-qc↗

arXiv2021

Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries

A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the "small" body is treated as a point particle of mass $m_p$ moving in the gravitational field generated by the large mass $M$, and one keeps only linear terms in the small mass ratio $m_p/M$. This technique usually yields finite answers, which are often in good agreement with fully nonlinear numerical relativity results, even when extrapolated to nearly comparable mass ratios. Here we study two situations in which the point-particle approximation yields a divergent result: the instantaneous flux emitted by a small body as it orbits the light ring of a black hole, and the total energy absorbed by the horizon when a small body plunges into a black hole. By integrating the Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time domains we show that both of these quantities diverge. We find that these divergences are an artifact of the point-particle idealization, and are able to interpret and regularize this behavior by introducing a finite size for the point particle. These divergences do not play a role in black-hole imaging, e.g. by the Event Horizon Telescope.

gr-qc↗

arXiv2021

Scalar and Gravitational Transient "Hair" for Near-Extremal Black Holes

We study the existence and nature of Aretakis "hair" 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-Nordstrom (NERN) and Kerr (NEK). 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 non-extremal 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.

gr-qc↗

arXiv2021

Gravitational tuning forks and hierarchical triple systems

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are an outstanding probe of strong-field physics and of the BH nature of compact objects.

gr-qc↗

arXiv2021

Genetic-algorithm-optimized neural networks for gravitational wave classification

Gravitational-wave detection strategies are based on a signal analysis technique known as matched filtering. Despite the success of matched filtering, due to its computational cost, there has been recent interest in developing deep convolutional neural networks (CNNs) for signal detection. Designing these networks remains a challenge as most procedures adopt a trial and error strategy to set the hyperparameter values. We propose a new method for hyperparameter optimization based on genetic algorithms (GAs). We compare six different GA variants and explore different choices for the GA-optimized fitness score. We show that the GA can discover high-quality architectures when the initial hyperparameter seed values are far from a good solution as well as refining already good networks. For example, when starting from the architecture proposed by George and Huerta, the network optimized over the 20-dimensional hyperparameter space has 78% fewer trainable parameters while obtaining an 11% increase in accuracy for our test problem. Using genetic algorithm optimization to refine an existing network should be especially useful if the problem context (e.g. statistical properties of the noise, signal model, etc) changes and one needs to rebuild a network. In all of our experiments, we find the GA discovers significantly less complicated networks as compared to the seed network, suggesting it can be used to prune wasteful network structures. While we have restricted our attention to CNN classifiers, our GA hyperparameter optimization strategy can be applied within other machine learning settings.

gr-qc↗