13. Breakdown of hydrodynamic universality in causal first-order viscous neutron star oscillations
Lennox S. Keeble (WFU), Alejandro Cárdenas-Avendaño (WFU)
Hydrodynamic modeling of viscous neutron stars requires a choice of theory of relativistic hydrodynamics. That distinct formulations contain the same physical content in the long-wavelength limit is referred to as “hydrodynamic universality.” It has been recently shown that hydrodynamic universality can break down in radial neutron star oscillations: causality and finite-size effects restrict access to the long-wavelength universal hydrodynamic regime in sufficiently viscous stars. We show that this breakdown occurs for a broad range of causal hydrodynamic frames in Bemfica–Disconzi–Noronha–Kovtun (BDNK) theory. Increasing viscosity collectively pushes this class of causal frames away from the BDNK regime of validity, eventually forcing all to lie outside it at large bulk viscosities. In this work we find that this breakdown of universality is accompanied by material changes in the oscillation mode structure: non-hydrodynamic modes become damped on timescales comparable to those of hydrodynamic modes, the first overtone can become longer lived than the fundamental mode, and unphysical instabilities with sub-millisecond timescales can emerge. Even in regimes where universality has broken down, we find that the inviscid threshold of gravitational collapse remains unchanged in BDNK theory. Our results provide evidence that first-order theories of relativistic hydrodynamics may be insufficient for modeling sufficiently viscous neutron stars.
Lennox is a graduate student in my group.
12. Quadratic Gravitational-Wave Scattering by Kerr Black Holes
Daniel C. M. Palumbo, Alejandro Cárdenas-Avendaño (WFU), Lena Murchikova
Of the two black holes, M87∗ and Sgr A∗, for which event-horizon-scale imaging is currently achievable, only Sgr A∗ at our Galactic Center exhibits sub-hour variability, making light curve observations of the inner accretion flow especially valuable for time-domain studies of the spacetime and the surrounding plasma. Observed light curves are often sampled with variable cadence, so a structure function is often used to quantify their variability properties. In this work, we assemble a heterogeneous Sgr A∗ light curve data set from discrete observations acquired over 12 years at 230 GHz, with different instruments, durations, and cadences, and study its structure function in three frameworks. First, we consider analytic predictions for the features of structure functions of stationary random processes with Fourier spectra dictated by the Matérn covariance. We then study the structure functions resulting from lensed movies of synthetic optically thin accretion flows approximated with Matérn covariance in both space and time, and identify which features in the structure function can be attributed to the black-hole geometry. Lastly, we examine the structure functions of a library of 72 general relativistic magnetohydrodynamic simulations. We find that, in general, magnetically arrested disk (MAD) models produce smoother structure functions with steeper slopes than standard and normal evolution (SANE) counterparts. On time scales of 5−15 minutes, the observed structure function slope of Sgr A∗ more closely aligns with the MAD trend, while both simulation types are generally more variable than the data on all sub-hour timescales.
11. Bayesian Evidence for Inspiraling Hotspot Motion in the Galactic Center
Pablo Ruales (WFU), Maciek Wielgus, Delilah E.A. Gates, Alejandro Cardenas-Avendano (WFU)
In this work, we develop a Bayesian framework to infer the time-dependent kinematics of the hotspot from polarized light curves, using a general prescription for its motion. We model the emitting region’s trajectory as a continuous, piecewise sequence of K kinematic segments, each described by radial and azimuthal velocity parameters. We perform analyses with K=1,2,3 and compare these models to millimeter-wavelength ALMA observations of Sgr A* from 2017 April 11 that include two subsequent Q-U loops, extending the observational constraints on the kinematics. We find statistically significant evidence that the emitting region follows a non-geodesic inspiraling trajectory, and this preference over a strictly Keplerian orbit strengthens sharply when a longer data segment is modeled. Our results offer new insight into the nature of flaring events in the Galactic Center and the episodically produced hotspots associated with them.
Pablo is a graduate student in my group.
10. Quadratic Gravitational-Wave Scattering by Kerr Black Holes
Lennox Keeble (WFU), Hengrui Zhu, Lawrence E. Kidder, Harald P. Pfeiffer & Mark A. Scheel
In this work Lennox and collaborators use numerical relativity to study the quadratic response of Kerr black holes to nearly monochromatic (ℓ,m) = (2,±2) incident gravitational waves, measuring the complex self-coupling to the outgoing (ℓ,m) = (4,4) daughter at twice the parent frequency for black-hole spins up to a = 0.95. At low frequencies, the coupling is strongly suppressed and exhibits opposite spin dependence for prograde and retrograde scattering. At higher prograde frequencies, they identify a daughter-mode resonance whose frequency and width extracted from the nonlinear response track the fundamental (ℓ,m,n) = (4,4,0) QNM. Near the fundamental (2,2,0) QNM frequency, the in-mode coupling grows with spin, in contrast to the decreasing quadratic QNM coupling, demonstrating that the nonlinear response depends on the full parent scattering state rather than on its frequency alone. These numerical-relativity results and their semi-analytic extension provide a basis for generic homogeneous radiative perturbations of Kerr at second order, with applications to dynamical tides, near-extremal dynamics, and second-order gravitational self-force theory.
Lennox is a graduate student in my group.
9. A Systematic Study of Resonance-Driven Flux Modifications in Extreme-Mass-Ratio Inspirals
Edoardo Levati (WFU), Lennox Keeble (WFU) and Alejandro Cárdenas-Avendaño (WFU)
In this work, we present, to our knowledge, the most extensive systematic analysis to date of resonant modifications to the energy, axial angular momentum, and Carter constant fluxes across a broad region of orbital parameter space. We use the publicly available pybhpt code to solve the frequency-domain Teukolsky equation and implement the resonant-flux formalism of Flanagan, Hughes, Ruangsri, coherently combining the degenerate harmonics at resonance. We analytically show that the minimum number of cycles in the resonance coefficients over phase for
a βθ:βr resonance is given by lcm(2,βr). Beyond this selection rule, we identify three novel behaviors of the resonance coefficients. First, all resonances considered admit phases at which the coefficients vanish simultaneously. Second, the coefficients span all possible sign combinations across the configurations explored. Depending on the orbital parameters and resonance, all three fluxes can be enhanced, all three suppressed, or some enhanced and others suppressed relative to their non-resonant values. Third, owing to our systematic exploration of the parameter space, we found that the coefficients associated with angular momentum and Carter constant can exhibit non-monotonic behavior, with local minima arising due to cancellations between the horizon and infinity contributions. Our results constitute the largest set of Teukolsky-based resonance coefficients calculated to date and provide essential input for future studies of transient orbital resonances in EMRIs.
Edoardo and Lennox are graduate students in my group.
8. A Four-Dimensional Gaussian Random Field Generator for Modeling Spatiotemporal Variability in Astrophysical Sources
Alejandro Cárdenas-Avendaño (WFU), Diego Rubiera-Garcia & Frederic H. Vincent
Semi-analytic models of black-hole movies require both an emitting flow prescription and a time-dependent source variability. Existing prescriptions are often limited to either equatorial emission or time-independent sources. In this work we present a unified model for these two ingredients. First, we prescribe an off-equatorial, nongeodesic Kerr fluid rotation law by lifting an equatorial specific-angular-momentum profile to cylindrical surfaces, setting the polar component of the four-velocity to zero, normalizing the flow with the full Kerr metric at the spacetime point, and retaining the option to recover a geodesic-like plunging prescription when needed. Second, we use this velocity as the disk advection field in a four-dimensional inhomogeneous, anisotropic Mat\’ern-like Gaussian random field. We provide a parametrized model for a torus-like disk and a central jet through a single composite correlation tensor. The resulting effective model is an implementation-ready prescription for time-dependent thick-disk and disk-jet emission for relativistic studies.
7. Light Propagation Prescriptions for Black Hole Movies
Daniel Rojas-Paternina & Alejandro Cárdenas-Avendaño (WFU)
In this work, we study light propagation prescriptions for simulating black hole movies, and show how the relevance of “slow” light is controlled by the competition between source variability and geodesic delay structure. In this work, we have proposed brisk light: a practical reduced-delay prescription for computing black-hole movies. It uses the ray-traced delay distributions to identify the dominant temporal support of each lensing band, then evaluates the same source movie with a clipped version of the slow-light time map. Because a single global source snapshot erases the relative timing between lensing bands, even the modal brisk limit can outperform fast light under this prescription. The proposed methodology provides both a practical criterion for when slow light matters and an efficient route to black hole movies that retain the leading temporal imprint of strong lensing, a regime of direct relevance for future space-based VLBI targeting photon-ring observables.
This work was based on Daniel’s undergraduate thesis at Universidad Nacional de Colombia, which I supervised.
6. Parameter-estimation bias induced by transient orbital resonances in extreme-mass-ratio inspirals
Edoardo Levati (WFU) & Alejandro Cárdenas-Avendaño (WFU)
In this work, we assess the parameter bias induced by transient orbital resonances with orbit-dependent coefficients and representative sign
assignments. In particular, we focus on the most dynamically significant low-order resonances, the 3 : 2 and the 2 : 1, as well as on the high-order, subdominant resonances, the 3 : 1 and the 4 : 3. We find that, for most of the orbits we study, spanning low to moderate eccentricities and inclinations, neglecting the effect of a resonance crossing induces a significant bias in parameter estimation. Our results provide further evidence that failing to model transient orbital resonances accurately can hinder EMRI detection and parameter estimation, thereby limiting their scientific potential.
Edoardo is a graduate student in my group.
5. Sensitivities of Black Hole Images from GRMHD Simulations
Pedro Naethe Motta, Mário Raia Neto, Cora Prather, Alejandro Cárdenas-Avendaño (WFU)
In this work, for the first time, we compute sensitivities for black hole images obtained from GRMHD snapshots, and use them to conduct gradient-based fitting experiments as illustrative applications for black hole imaging. Sensitivities are pixel-wise derivatives of the intensity with respect to model parameters, which form the Jacobian of the forward model and define a local map from parameter space to image space. This work establishes a basis for efficient, high-precision model–data comparisons in black hole imaging and motivates the integration of these sensitivities into advanced inference frameworks.
Pedro and Mário are graduate students in Brazil that worked under the guidance of Cora and me.
4. Polarization Signatures of Inspiraling Hotspots around Kerr Black Holes
Pablo Ruales (WFU), Delilah E. A. Gates, Alejandro Cárdenas-Avendaño (WFU)
In this paper, we revisited the anatomy of the loop generated by Stokes parameters 𝑄 and 𝑈 that describe the polarized intensity on the observer’s screen, the so-called 𝑄–𝑈 loops, and computed them, for the first time, for inspiraling hotspots outside the ISCO. Compared to perpetual hotspots, i.e., hotspots on stable orbits at constant radius, inspiraling hotspots naturally produce a richer, time-dependent morphology while still exhibiting the characteristic loop-like behavior on orbital timescales. This modeling is especially relevant given that previous works have shown that perpetual hotspots can only account for an initial primary loop, whereas additional data points often fall inside the primary loop, a morphology that inspiraling trajectories can naturally generate. This model can be applied to current and near-future interferometric observations of linear polarization, offering a new avenue to probe the physics of matter spiraling inward and the relativistic velocities of plunging plasma.
Pablo is a graduate student in my group.
3. 𝙹𝚒𝚙𝚘𝚕𝚎: A Differentiable 𝚒𝚙𝚘𝚕𝚎-based Code for Radiative Transfer in Curved Spacetimes
Pedro Naethe Motta, Ben S. Prather, Alejandro Cárdenas-Avendaño (WFU)
This paper introduces 𝙹𝚒𝚙𝚘𝚕𝚎, a new computational tool based on the existing 𝚒𝚙𝚘𝚕𝚎 code, for simulating how light travels through curved spacetime. Unlike traditional methods that rely on generating large sets of model images and comparing them to observations, Jipole is automatically differentiable, meaning it can calculate how small changes in input parameters (like a black hole’s spin or the viewer’s angle, as we studied in this work) affect the resulting image. This approach yields gradients that can significantly speed up fitting theoretical models to observational data. We have validated 𝙹𝚒𝚙𝚘𝚕𝚎 against standard (non-differentiable) approaches and showed that it produces accurate gradients. As proof of concept, we also show how these gradients can be used in optimization routines to recover model parameters, even when images are blurred or noisy, with just a few steps (images computed). Overall, 𝙹𝚒𝚙𝚘𝚕𝚎 offers a more efficient path for interpreting high-resolution black hole images, which could enable faster and more reliable parameter estimation.
In the summer of 2025, Pedro, a graduate student in São Paulo, led this research under the guidance of Cora and me.
2. Estimating High-Order Time Derivatives of Kerr Orbital Functionals
Lennox S. Keeble, Alejandro Cárdenas-Avendaño (WFU)
In this paper we develop practical methods for calculating higher-order time derivatives of quantities defined along particle orbits around a rotating (Kerr) black hole. Such derivatives are needed, for example, to model gravitational wave signals from systems where a small compact object spirals into a massive black hole. In this work we describe two approaches: one uses a change of variables and Fourier expansion to map from an auxiliary time parameter to physical time, while the other directly fits orbital data to a truncated Fourier series. We show that both methods can reliably estimate derivatives up to sixth order with only a modest number of Fourier modes. These results make it easier to build efficient approximate waveform models and to track how orbital quantities evolve due to gravitational radiation.
Lennox worked under my guidance in the spring and summer of 2025.
1. Cumulative effect of orbital resonances in extreme-mass-ratio inspirals
Edoardo Levati (WFU), Alejandro Cárdenas-Avendaño, Kyriakos Destounis & Paolo Pani
This paper examines how repeated orbital resonances affect the evolution of extreme-mass-ratio inspirals (EMRIs). We employ an effective resonance model that builds in analytical corrections to the gravitational-wave–driven radiation reaction rates. We find that treating all resonances with a single, universal shift across all conserved quantities, as previously done, overstates their overall effect. Instead, each resonance crossing needs its own adjustment. Accounting for these individualized corrections reveals that the cumulative impact of multiple resonances—especially for highly eccentric orbits—can significantly alter the inspiral’s trajectory. These findings underscore the importance of including detailed resonance modeling when constructing waveform templates to accurately extract astrophysical information from future EMRI detections.
Edoardo began this research as part of his Master’s thesis at La Sapienza, with guidance from Kyriakos, Paolo, and me. He completed this work while he was at Wake Forest University under my supervision.