arXiv subjects

Abhishek Hegade K. R.

Publications and source records attributed to Abhishek Hegade K. R..

18 recordsLinked to original sources

arXiv2026

Nonlinear Perturbations of Relativistic Stars

We extend the general relativistic Lagrangian perturbation formalism of Friedman and Schutz [Astrophys. J. 200, 204 (1975)] beyond linear order, retaining full time dependence of the perturbations. We provide general formulae to relate the Lagrangian and Eulerian perturbations to any general perturbative order. As a proof of principle, we apply the framework to tidally perturbed relativistic stars in Regge-Wheeler gauge and reduce the second-order field and conservation equations to master equations with a nonlinear source. Projecting the source onto the star's eigenmodes, we obtain a nonlinear equation of motion for the mode amplitudes and the coupling coefficients, which describe the interactions among the eigenmodes and with the external tidal field. Approximating the tidal field and the coupling coefficients, we compute the static quadratic Love number from the quadrupolar fundamental mode alone and find that it reproduces the direct metric-matching value to a reasonable accuracy of $4\%$, up to a further correction arising from the Hamiltonian and momentum constraints of the second-order tidal field.

gr-qc↗

arXiv2026

Dynamical tidal response of neutron stars as a probe of dense-matter properties

Dynamical tidal deformations play a crucial role in the gravitational waves emitted by binary neutron star systems during their late inspiral. In this work, we systematically explore how relativistic (dynamical and dissipative) tidal deformations depend on the internal structure of a neutron star using two analytic classes of equations of state. The first class is a nucleonic model that is parameterized by nuclear physics observables, such as the symmetry energy coefficients and saturation properties. The second class is a toy model of quark matter, the MIT bag model. To model tidal dissipation, we self-consistently include contributions from weak-interaction-driven bulk-viscous effects while considering both the nucleonic and the quark-matter equations of state. The dissipative tide is sensitive to frequency and temperature, but its magnitude, as predicted by weak-interaction-driven bulk-viscous effects, is too small (within the equation-of-state models studied here) to be detectable by current or future observations. However, we find that the (conservative) dynamical tidal response function depends strongly on the slope of the symmetry energy and on higher-order coefficients of the symmetry energy. This indicates that the (conservative) dynamical tide is sensitive to higher-order coefficients, motivating a dedicated parameter-estimation study to assess how well they can be constrained.

gr-qc↗

arXiv2026

Extreme-Mass-Ratio Inspirals in Gaseous Disks

Gravitational waves from extreme mass ratio inspirals (EMRIs) are precise probes of the environment of the supermassive black holes (SMBHs) they orbit. If an SMBH is actively accreting, the surrounding gaseous disk can impart hydrodynamic torques on and assist the formation of EMRIs within it. Such disk-EMRI interactions could leave measurable imprints on future observations by the Laser Interferometer Space Antenna (LISA), and potentially provide a route to constrain disk properties using gravitational wave observations. We present herein a detailed relativistic analysis of these hydrodynamic interactions using linear theory. We first derive a Lagrangian governing the evolution of spiral density waves in the disk and use it to formulate a balance law for the transfer of angular momentum between the EMRI and disk. We then develop a stable numerical scheme which can be used to treat corotation resonances and find modal solutions in thin disks up to very large azimuthal numbers. Using this numerical scheme, we explore how SMBH spins, EMRI semi-major axes, disk scale heights, sound speed gradients, and surface density gradients affect the interaction between accretion disks and circular EMRIs. Our results show that relativistic effects substantially alter disk-EMRI interactions once the secondary orbit is within $\mathcal{O}(25)$ Schwarzschild radii from the SMBH. Comparing our numerical results with recent analytical models suggests that the impact of pressure gradients and softening of the gravitational potential is important for disks with finite thickness and cannot be captured by tuning the torque cutoff parameters in the analytical models. The framework provided here will help analyze the formation scenarios of EMRIs and build relativistically accurate waveform models of disk-EMRI interactions.

astro-ph.HE↗

arXiv2026

Swing amplification in star-gas disks

Recent JWST and ALMA observations have revealed stellar bars and spirals in gas-rich galactic disks at redshifts as high as $z \simeq 4$. The simplest theoretical paradigm we have for understanding such non-axisymmetric features is the linear theory of swing amplification (SA) in the 2D shearing sheet. However, while the SA mechanism in a gaseous shearing sheet was first studied in 1965, and that in a collisionless stellar sheet in 1966, the coupled star-gas linear SA equations have never been solved explicitly. Here we write down these equations and use them to study the evolution of non-axisymmetric swinging waves in stable disks. We find that waves are often amplified temporarily by factors of $10-100$ or more, and that the maximum \textit{non-axisymmetric} amplification factor is tightly correlated with the system's distance from the \textit{axisymmetric} stability boundary in the $(1/Q_\mathrm{s}, 1/Q_\mathrm{g})$ plane. The true star-gas behavior differs significantly from the `two-fluid' idealizations used in the past, because phase mixing of the collisionless stellar component acts as a sink of perturbation energy. Closely analogous results hold for finite-thickness disks except for the shifting of the stability boundary. We provide a \texttt{python} code that calculates the SA factors and maximally-amplified wavelength given the background disk parameters.

astro-ph.GA↗

arXiv2026

A New Spin on Dissipative Tides: First-Post-Newtonian Effects in Compact Binary Inspirals

Tidal dissipation in spinning compact binaries imprints characteristic corrections on the late-inspiral gravitational-wave signal. We develop a next-to-leading order post-Newtonian description of dissipative, electric-quadrupolar tides in spinning compact binaries, deriving the center-of-mass equations of motion, a generalized energy-balance law, and the corresponding Fourier-phase correction for quasi-circular orbits with spins aligned or anti-aligned with the orbital angular momentum. Using the most general, low-frequency, linear tidal response compatible with rotational symmetry, we show that spin-induced tidal dissipation enters the gravitational-wave phase at 2.5 post-Newtonian order and carries a logarithmic frequency dependence, so it is not degenerate with the coalescence phase. For binary black holes, our dissipative flux reproduces horizon absorption in the extreme-mass-ratio limit. These results provide new waveform ingredients for precision modeling of spinning compact binaries in the high-signal-to-noise era.

gr-qc↗

arXiv2026

Universal Relations with Dynamical Tides

Observations of neutron stars and the precise measurement of their macroscopic properties have provided valuable insights into fundamental physics, both by constraining the behavior of nuclear matter under extreme conditions and by enabling tests of general relativity in the strong-field regime. In this context, equation-of-state-insensitive or ``quasi-universal'' relations between key observables, such as the compactness, dimensionless static tidal deformability, and moment of inertia, play a crucial role in connecting different measurable observables while minimizing uncertainties due to the yet unknown equation-of-state. In this work, we identify new quasi-universal relations between the static, dimensionless tidal deformability ($Λ^{(0)}$) and its leading-order dynamical correction ($Λ^{(2)}$), as well as between $Λ^{(0)}$ and a combination of these parameters ($\sqrt{ Λ^{(0)}/Λ^{(2)}}\equiv Mω_*$), obtained from the small-frequency expansion of the relativistic tidal response. We test these relations across a representative set of 59 equations of state, finding that the equation-of-state dependence does not exceed $\sim$5\% for the $Λ^{(0)}$--$Λ^{(2)}$ relation and $\sim2.8\%$ for the $Λ^{(0)}$--$Mω_*$ relation. This indicates a high degree of universality and offers a simplified framework for incorporating dynamical tidal effects into gravitational-wave modeling. Furthermore, we compare the dynamical tidal response against different recent strategies (a Taylor expansion and a one-mode approximation) to model the dynamical tide. We find that both models are capable of capturing the frequency-dependent behavior of the dynamical tidal deformability, with the one-mode approximation agreeing better with the dynamical response than the Taylor expansion in most of the parameter space.

gr-qc↗

arXiv2026

The Good, the Bad, and the Subtle: Relativistic mode sums for neutron-star tidal response

Time-dependent tidal interactions during the late inspiral of binary neutron stars encode valuable information about neutron-star structure, but systematically extending the familiar Newtonian mode-sum picture into full general relativity is nontrivial. In this paper, we develop a practical relativistic implementation of mode-sum tidal response for non-rotating neutron stars in Regge-Wheeler gauge. Using near-zone boundary conditions, we systematically define the interior tidal field, the relativistic overlap integrals, and the corresponding mode amplitudes. The good is that the dominant f-mode contribution is remarkably robust, reproducing the direct matching calculation to within $\sim 3$\% across the equations of state we consider. The bad is that the operator governing mode inner product is not positive definite on the full Regge-Wheeler-gauge function space, so the relativistic mode sum truncated at ${\cal{O}}(ω^2)$ is not expected to strictly converge to the direct matching solution. The subtle is that the tidal field inside the star is not unique, although this ambiguity has only a limited impact on the dominant f-mode response for the classes of extensions studied here. Our results establish the practical utility of relativistic mode-sum approximations, while making clear that their predictive power comes from a controlled low-mode description, rather than from a formally convergent strong-field expansion.

gr-qc↗

arXiv2026

Kinetic magnetohydrodynamics and Landau fluid closure in relativity

Diffuse accretion flows near a supermassive black hole are fundamentally weakly collisional. In such weakly collisional plasmas, the ion and electron distribution functions can deviate significantly from thermal equilibrium, and particle kinetic effects can influence large-scale fluid motion by driving pressure anisotropy, heat conduction, and plasma instabilities. Modeling these plasma effects in highly relativistic flows could be important for interpreting horizon-scale observations of black hole images. In this paper, we present a theoretical framework for understanding weakly collisional plasmas in general relativity by deriving the relativistic drift kinetic equations from the Vlasov-Maxwell equations. We present the evolution equations for the moments of the gyroaveraged distribution function and introduce a new analytic Landau fluid closure to capture anisotropic heat flow in relativistic plasmas. Unlike standard (collisional) general relativistic magnetohydrodynamics or extended magnetohydrodynamics, our model does not rely on strong collisions to enforce thermal equilibrium and consistently incorporates Landau damping in a fluid closure. The model introduced in this work provides a complementary approach to fully kinetic simulations in understanding weakly collisional effects in low-luminosity relativistic black hole accretion disks.

astro-ph.HE↗

arXiv2026

Relativistic and Dynamical Love

Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and prove that the dynamical tidal response can be expanded in a complete set of modes. We further prove that the mode amplitudes satisfy an effective, forced harmonic oscillator equation, which generalizes the overlap-integral formulation of Newtonian gravity. Our relativistic treatment of dynamical tides will avoid systematic biases in future gravitational-wave parameter estimation.

gr-qc↗

arXiv2026

A relativistic treatment of accretion disk torques on extreme mass ratio inspirals around spinning black holes

We model the motion of a small compact object on a nearly circular orbit around a spinning supermassive black hole, which is also interacting with a thin equatorial accretion-disk surrounding the latter, through tools from self-force and Hamiltonian perturbation theory. We provide an analytical and relativistically-accurate formalism to calculate the rate of energy and angular momentum exchanged at Lindblad resonances. We show that strong relativistic effects can potentially cause a reversal in the direction of the torque on the small compact object if the surface density gradient is not too large. We analytically explore the dependence of the torque reversal location on the spin of the supermassive black hole and demonstrate that the ratio of the reversal location to the innermost stable circular orbit is approximately insensitive to the spin of the supermassive black hole. Our results show that relativistic torques can be 1--2 order of magnitude larger than the Newtonian torque routinely used in the literature to model disk/small-compact-object interactions close to the supermassive black hole. Our results highlight the importance of including relativistic effects when modeling environmental effects in extreme mass-ratio inspirals.

gr-qc↗

arXiv2026

A relativistic treatment of accretion disk torques on extreme mass-ratio inspirals around non-spinning black holes

We develop a relativistically accurate formalism to model the interaction between stellar mass compact objects embedded in thin accretion disks around a non-spinning supermassive black hole, using tools from self-force theory and Hamiltonian perturbation theory. We then apply this formalism to analyze the evolution of a compact object on a nearly circular and equatorial orbit interacting with a thin equatorial disk. We provide analytic and relativistically-accurate expressions for the rates of energy and angular momentum exchanged during interactions due to Lindblad and corotation resonances. Our results show that relativistic corrections can enhance the magnitude of the torque by 1-2 orders of magnitude compared to purely Newtonian expressions when the orbit of the compact object is smaller than $10$ Schwarzschild radii of the supermassive black hole. We also demonstrate that strong relativistic shifts the inner Lindblad resonances closer to the compact object than the outer Lindblad resonances when the compact object is closer than 4 Schwarzschild radii to the supermassive black hole, potentially leading to a reversal in the direction of the torque acting on the compact object. Finally, we provide a dephasing estimate and show that using the relativistic torque formula is crucial to obtain reliable estimates for extreme mass ratio inspirals in orbits closer than 5 Schwarzschild radii to the supermassive black hole. Our results highlight the importance of using relativistically-accurate models of environmental interactions in extreme mass-ratio inspirals close to a supermassive black hole.

gr-qc↗

arXiv2025

Large Average Subtensor Problem: Ground-State, Algorithms, and Algorithmic Barriers

We introduce the large average subtensor problem: given an order-$p$ tensor over $\mathbb{R}^{N\times \cdots \times N}$ with i.i.d. standard normal entries and a $k\in\mathbb{N}$, algorithmically find a $k\times \cdots \times k$ subtensor with a large average entry. This generalizes the large average submatrix problem, a key model closely related to biclustering and high-dimensional data analysis, to tensors. For the submatrix case, Bhamidi, Dey, and Nobel~\cite{bhamidi2017energy} explicitly highlight the regime $k=Θ(N)$ as an intriguing open question. Addressing the regime $k=Θ(N)$ for tensors, we establish that the largest average entry concentrates around an explicit value $E_{\mathrm{max}}$, provided that the tensor order $p$ is sufficiently large. Furthermore, we prove that for any $γ>0$ and large $p$, this model exhibits multi Overlap Gap Property ($m$-OGP) above the threshold $γE_{\mathrm{max}}$. The $m$-OGP serves as a rigorous barrier for a broad class of algorithms exhibiting input stability. These results hold for both $k=Θ(N)$ and $k=o(N)$. Moreover, for small $k$, specifically $k=o(\log^{1.5}N)$, we show that a certain polynomial-time algorithm identifies a subtensor with average entry $\frac{2\sqrt{p}}{p+1}E_{\mathrm{max}}$. In particular, the $m$-OGP is asymptotically sharp: onset of the $m$-OGP and the algorithmic threshold match as $p$ grows. Our results show that while the case $k=Θ(N)$ remains open for submatrices, it can be rigorously analyzed for tensors in the large $p$ regime. This is achieved by interpreting the model as a Boolean spin glass and drawing on insights from recent advances in the Ising $p$-spin glass model.

math.ST↗

arXiv2025

Dissipative tidal effects to next-to-leading order and constraints on the dissipative tidal deformability using gravitational wave data

Dissipative tidal interactions can be used to probe the out-of-equilibrium physics of neutron stars using gravitational wave observations. In this paper, we present the first post-Newtonian (PN) corrections to the orbital dynamics of a binary system containing objects whose tidal interactions have a dissipative contribution. We derive the 1PN-accurate equations of motion in the center-of-mass frame and a generalized energy-balance law that is valid for dissipative tidal interactions. We show how mass and energy loss due to the absorption of orbital energy change the orbital dynamics and derive the next-to-leading order correction to the gravitational wave phase of a binary system in a quasi-circular orbit containing initially non-spinning components. We then use this waveform model to constrain, for the first time, the individual dissipative tidal deformabilities of each of the binary components that generated the GW170817 event using real data. We find that the GW170817 data requires $Ξ_{1} \lesssim 1121$ and $Ξ_{2} \lesssim 1692$ at 90\% confidence, where $Ξ_{1,2}$ are the individual tidal deformabilities of the primary and secondary binary components that produced the GW170817 event.

gr-qc↗

arXiv2025

Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neutron star binaries

We study the impact of out-of-equilibrium, dissipative effects on the dynamics of inspiraling neutron stars. We find that modeling dissipative processes (such as those from the stars internal effective fluid viscosity) requires that one introduce a new tidal deformability parameter--the dissipative tidal deformability--which modifies the phase of gravitational waves emitted during the inspiral phase of a neutron star binary. We show that the dissipative tidal deformability corrects the gravitational-wave phase at 4 post-Newtonian order for quasi-circular binaries. This correction receives a large finite-size enhancement by the stellar compactness, analogous to the case of the tidal deformability. Moreover, the correction is not degenerate with the time of coalescence, which also enters at 4PN order, because it contains a logarithmic frequency-dependent contribution. Using a simple Fisher analysis, we show that physically allowed values for the dissipative tidal deformability may be constrained by measurements of the phase of emitted gravitational waves to roughly the same extent as the (electric-type, quadrupolar) tidal deformability. Finally, we show that there are no out-of-equilibrium, dissipative corrections to the tidal deformability itself. We conclude that there are at least two relevant tidal deformability parameters that can be constrained with gravitational-wave phase measurements during the late inspiral of a neutron star binary: one which characterizes the adiabatic tidal response of the star, and another which characterizes the leading-order out-of-equilibrium, dissipative tidal response. These findings open a window to probe dissipative processes in the interior of neutron stars with gravitational waves.

gr-qc↗

arXiv2024

First constraint on the dissipative tidal deformability of neutron stars

The gravitational waves (GWs) emitted by neutron star binaries probe the physics of matter at supra nuclear densities. During the late inspiral, tidal deformations raised on each star by the gravitational field of its companion depend crucially on the star's internal properties. The misalignment of a star's tidal bulge with its companion's gravitational field encodes the strength of internal dissipative processes, which imprint onto the phase of the gravitational waves emitted. We here analyze GW data from the GW170817 (binary neutron star) event detected by LIGO and Virgo and find the first constraint on the dissipative tidal deformability of a neutron star. From this constraint, \emph{assuming} a temperature profile for each star in the binary, we obtain an order of magnitude bound on the averaged bulk ($ζ$) and shear ($η$) viscosity of each star during the inspiral.: $ζ\lesssim 10^{31} \mathrm{g}\;\mathrm{cm}^{-1}\mathrm{s}^{-1}$ and $η\lesssim 10^{28} \mathrm{g}\;\mathrm{cm}^{-1}\mathrm{s}^{-1} $. We forecast that these bounds could be improved by two orders of magnitude with third-generation detectors, like Cosmic Explorer, using inspiral data. These constraints already inform nuclear physics models and motivate further theoretical work to better understand the interplay between viscosity and temperature in the late inspiral of neutron stars.

gr-qc↗

arXiv2024

Dynamical tidal response of non-rotating relativistic stars

Accurately modeling the tidal response of neutron stars is crucial to connecting gravitational wave observations of binaries to ultra-dense nuclear physics. Most current models of the tidal response of relativistic stars either assume a static response model, or use phenomenological models inspired by Newtonian gravity. In this work, we present a general formalism for computing the linear dynamical tidal response function of relativistic, spherically symmetric stars. Our formalism incorporates stratification due to thermal and chemical imbalances, allowing one to study the effects of g modes on the tidal response function. We also describe how to incorporate sources of dissipation due to shear and bulk viscosity. To showcase the utility of our approach, we present several applications for polytropic stars in general relativity. We show how our formalism can capture the dynamical tidal resonance due to the f and g modes of inviscid stars and explore the sensitivity of the dynamical tidal response to the compactness of the star. We also compute the dissipative tidal deformability due to bulk and shear viscous dissipation assuming a simple viscous profile for the bulk and shear viscosity.

gr-qc↗

arXiv2022

How Do Spherical Black Holes Grow Monopole Hair?

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this paper, we study this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing Oppenheimer-Snyder background, and (ii) a collapsing neutron star background. In case (i), we find an exact scalar field solution analytically, while in case (ii) we solve for the temporal evolution of the scalar field numerically, with both cases supporting the conclusion presented above. Our results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.

gr-qc↗

arXiv2021

Cosmology with Love: Measuring the Hubble constant using neutron star universal relations

Gravitational-wave cosmology began in 2017 with the observation of the gravitational waves emitted in the merger of two neutron stars, and the coincident observation of the electromagnetic emission that followed. Although only a $30\%$ measurement of the Hubble constant was achieved, future observations may yield more precise measurements either through other coincident events or through cross correlation of gravitational-wave events with galaxy catalogs. Here, we implement a new way to measure the Hubble constant without an electromagnetic counterpart and through the use of the binary Love relations. These relations govern the tidal deformabilities of neutron stars in an equation-of-state insensitive way. Importantly, the Love relations depend on the component masses of the binary in the source frame. Since the gravitational-wave phase and amplitude depend on the chirp mass in the observer (and hence redshifted) frame, one can in principle combine the binary Love relations with the gravitational-wave data to directly measure the redshift, and thereby infer the value of the Hubble constant. We implement this approach in both real and synthetic data through a Bayesian parameter estimation study in a range of observing scenarios. We find that for the LIGO/Virgo/KAGRA design sensitivity era, this method results in a similar measurement accuracy of the Hubble constant to those of current-day, dark-siren measurements. For third generation detectors, this accuracy improves to $\lesssim 10\%$ when combining measurements from binary neutron star events in the LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era.

gr-qc↗