arXiv subjects

Rodrigo Panosso Macedo

Publications and source records attributed to Rodrigo Panosso Macedo.

At least 37 records · Page 2Linked to original sources

arXiv2025

The Confluent Heun functions in Black Hole Perturbation Theory: a spacetime interpretation

This work provides a spacetime interpretation of the confluent Heun functions within black hole perturbation theory (BHPT) and explores their relationship to the hyperboloidal framework. In BHPT, the confluent Heun functions are solutions to the radial Teukolsky equation, but they are traditionally studied without an explicit reference to the underlying spacetime geometry. Here, we show that the distinct behaviour of these functions near their singular points reflects the structure of key surfaces in black hole spacetimes. By interpreting homotopic transformations of the confluent Heun functions as changes in the spacetime foliation, we connect these solutions to different regions of the black hole's global structure, such as the past and future event horizons, past and future null infinity, spatial infinity, and even past and future timelike infinity. We also discuss the relationship between the confluent Heun functions and the hyperboloidal formulation of the Teukolsky equation. Although neither confluent Heun form of the radial Teukolsky equation can be interpreted as hyperboloidal slices, this approach offers new insights into wave propagation and scattering from a global black hole spacetime perspective.

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arXiv2025

Quadratic quasi-normal mode dependence on linear mode parity

Quasinormal modes (QNMs) uniquely describe the dominant piece of the gravitational-wave ringdown of postmerger black holes. While the linear QNM regime has been extensively studied, recent work has highlighted the importance of second-perturbative-order, quadratic QNMs (QQNMs) arising from the nonlinear coupling of linear QNMs. Previous attempts to quantify the magnitude of these QQNMs have shown discrepant results. Using a new hyperboloidal framework, we resolve the discrepancy by showing that the QQNM/QNM ratio is a function not only of the black hole parameters but also of the ratio between even- and odd-parity linear QNMs: the ratio QQNM/QNM depends on what created the ringing black hole, but only through this ratio of even- to odd-parity linear perturbations.

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arXiv2025

Hyperboloidal Approach to Quasinormal Modes

Oscillations of black hole spacetimes exhibit divergent behavior toward the bifurcation sphere and spatial infinity. This divergence can be understood as a consequence of the geometry in these spacetime regions. In contrast, black-hole oscillations are regular when evaluated toward the event horizon and null infinity. Hyperboloidal surfaces naturally connect these regions, providing a geometric regularization of time-harmonic oscillations called quasinormal modes (QNMs). This review traces the historical development of the hyperboloidal approach to QNMs. We discuss the physical motivation for the hyperboloidal approach and highlight current developments in the field.

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arXiv2024

Superradiant Instability of Magnetic Black Holes

Black hole superradiance has proven being very valuable in several realms of gravitational physics, and holds a promising discovery potential. In this paper, we consider the superradiant instability of magnetically-charged, rotating black holes and find a number of important differences with respect to neutral ones. Considering massive charged bosonic fields, we find that the instability timescale is much shorter, and this is true even if the black hole contains an order-one number of magnetic monopoles, or merely a single one, and possesses either low, moderate or large values of angular momentum. In particular, the instability is drastically faster than the radiative decay time of charged pions, potentially making it physically relevant. Furthermore, our analysis identifies the most unstable modes as a class of monopole spheroidal harmonics, that we dub north and south monopole modes, whose morphology is markedly different from the ones in standard superradiance since they extend along the rotational axis. For completeness, we also study the quasinormal mode spectrum and amplification factors of charged massless fields, finding no evidence of instabilities in that case.

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arXiv2024

Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order

Most self-force calculations rely, in one way or another, on representations of a particle's Detweiler- Whiting singular field. We present a simple method of calculating the singular field to high order in a local expansion in powers of distance from the particle. As a demonstration, we compute the singular field to 14th order in distance, 10 orders beyond the previous state of the art, in the simple case of a scalar charge in circular orbit around a Schwarzschild black hole. We provide the result in both a 4-dimensional form and a decomposed form suitable for use in an m-mode puncture scheme. Our method should have applications in overcoming bottlenecks in current self-force calculations at both first and second order in perturbation theory.

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arXiv2024

Multi-domain spectral method for self-force calculations

Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations are related to slow convergence of spherical-harmonic (or spheroidal harmonic) mode sums in a region containing the small companion. In this paper, we begin to develop a multi-domain framework that can evade those problems. Building on recent work by Osburn and Nishimura, in the problematic region of spacetime we use a puncture scheme and decompose the punctured field equations into a basis of Fourier and azimuthal $m$ modes, avoiding a harmonic decomposition in the $θ$ direction. Outside the problematic region, we allow for a complete spherical- or spheroidal-harmonic decomposition. As a demonstration, we implement this framework in the simple context of a scalar charge in circular orbit around a Schwarzschild black hole. Our implementation utilizes several recent advances: a spectral method in each region, hyperboloidal compactification, and an extremely high-order puncture.

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arXiv2024

On the physical significance of black hole quasinormal mode spectra instability

It has been shown, via specific examples and a pseudospectrum analysis, that the black hole quasinormal spectra are unstable. The implication of such a result for gravitational-wave physics and of our understanding of black holes is, still, unclear. The purpose of this work is twofold: (i) we show that some of the setups leading to instabilities are unphysical and triggered by exotic matter or extreme spacetimes; (ii) nevertheless, we also show simple examples of compelling physical scenarios leading to spectral instabilities. Our results highlight the importance of understanding the overtone content of time-domain waveforms, and their detectability.

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arXiv2024

Structural aspects of the anti-de Sitter black hole pseudospectrum

Black holes in anti-de Sitter spacetime provide an important testing ground for both gravitational and field-theoretic phenomena. In particular, the study of perturbations can be useful to further our understanding regarding certain physical processes, such as superradiance, or the dynamics of strongly coupled conformal field theories through the holographic principle. In this work we continue our systematic study of the ultraviolet instabilities of black-hole quasinormal modes, built on the characterization of the latter as eigenvalues of a (spectrally unstable) non-selfadjoint operator and using the pseudospectrum as a main analysis tool, extending our previous studies in the asymptotically flat setting to Anti-de Sitter asymptotics. Very importantly, this step provides a singularly well-suited probe into some of the key structural aspects of the pseudospectrum. This is a consequence of the specific features of the Schwarzschild-anti-de Sitter geometry, together with the existence of a sound characterization by Warnick of quasinormal modes as eigenvalues, that is still absent in asymptotic flatness. This work focuses on such structural aspects, with an emphasis on the convergence issues of the pseudospectrum and, in particular, the comparison between the hyperboloidal and null slicing cases. As a physical by-product of this structural analysis we assess, in particular, the spectral stability of purely imaginary ``hydrodynamic" modes, which appear for axial gravitational perturbations, that become dominant when the black-hole horizon is larger than the anti-de Sitter radius. We find that their spectral stability, under perturbations, depends on how close they are to the real axis, or conversely how distant they are from the first oscillatory overtone.

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arXiv2024

Pseudospectrum of de Sitter black holes

Pseudospectral analyses have broadened our understanding of ringdown waveforms from binary remnants, by providing insight into both the stability of their characteristic frequencies under environmental perturbations, as well as the underlying transient and non-modal phenomenology that a mode analysis may miss. In this work we present the pseudospectrum of scalar perturbations on spherically-symmetric black holes in de Sitter spacetimes. We expand upon previous analyses in this setting by calculating the pseudospectrum of Reissner-Nordström-de Sitter black holes, and revisit results regarding the stability of quasinormal modes under perturbations in several cases. Of particular note is the case of scalar quasinormal modes with angular parameter $\ell=0$, which possess a zero mode related to the presence of a cosmological horizon. We show that the non-trivial eigenfunction associated to this mode has a vanishing energy norm which poses a challenge in quantifying the magnitude of external perturbations to the wave equation's potential, as well as in calculating the pseudospectrum. Nonetheless, we present results which suggest that the spectral instability manifestation of $\ell=0$ scalar quasinormal modes is qualitatively the same as in other cases, in contrast to recent claims. We also analyze the stability of the fundamental mode for $\ell\ge1$, finding it to be spectrally stable, except for certain configurations in which a perturbation leads to a discontinuous overtaking of the fundamental unperturbed purely-imaginary mode by a perturbed complex quasinormal mode.

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arXiv2024

Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics

This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the Trautman-Bondi mass in terms of the hyperboloidal metric functions. Moreover, we apply this formalism to a class of wave equations commonly used in black-hole perturbation theory. Additionally, we provide a comprehensive derivation of the hyperboloidal minimal gauge, introducing two alternative approaches within this conceptual framework: the in-out and out-in strategies. Specifically, we demonstrate that the height function in the in-out strategy follows from the well-known tortoise coordinate by changing the sign of the terms that become singular at future null infinity. Similarly, for the out-in strategy, a sign change also occurs in the tortoise coordinate's regular terms. We apply the methodology to the following spacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensional black holes, black hole with matter halo, and Reissner- Nordström-de Sitter. From this heuristic study, we conjecture that the out-in strategy is best adapted for black hole geometries that account for environmental or effective quantum effects.

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arXiv2023

Hyperboloidal discontinuous time-symmetric numerical algorithm with higher order jumps for gravitational self-force computations in the time domain

Within the next decade the Laser Interferometer Space Antenna (LISA) is due to be launched, providing the opportunity to extract physics from stellar objects and systems, such as \textit{Extreme Mass Ratio Inspirals}, (EMRIs) otherwise undetectable to ground based interferometers and Pulsar Timing Arrays (PTA). Unlike previous sources detected by the currently available observational methods, these sources can \textit{only} be simulated using an accurate computation of the gravitational self-force. Whereas the field has seen outstanding progress in the frequency domain, metric reconstruction and self-force calculations are still an open challenge in the time domain. Such computations would not only further corroborate frequency domain calculations and models, but also allow for full self-consistent evolution of the orbit under the effect of the self-force. Given we have \textit{a priori} information about the local structure of the discontinuity at the particle, we will show how to construct discontinuous spatial and temporal discretisations by operating on discontinuous Lagrange and Hermite interpolation formulae and hence recover higher order accuracy. In this work we demonstrate how this technique in conjunction with well-suited gauge choice (hyperboloidal slicing) and numerical (discontinuous collocation with time symmetric) methods can provide a relatively simple method of lines numerical algorithm to the problem. This is the first of a series of papers studying the behaviour of a point-particle prescribing circular geodesic motion in Schwarzschild in the \textit{time domain}. In this work we describe the numerical machinery necessary for these computations and show not only our work is capable of highly accurate flux radiation measurements but it also shows suitability for evaluation of the necessary field and it's derivatives at the particle limit.

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arXiv2023

Pseudospectrum of horizonless compact objects: a bootstrap instability mechanism

Recent investigations of the pseudospectrum in black hole spacetimes have shown that quasinormal mode frequencies suffer from spectral instabilities. This phenomenon may severely affect gravitational-wave spectroscopy and limit precision tests of general relativity. We extend the pseudospectrum analysis to horizonless exotic compact objects which possess a reflective surface arbitrarily close to the Schwarzschild radius, and find that their quasinormal modes also suffer from an overall spectral instability. Even though all the modes themselves decay monotonically, the pseudospectrum contours of equal resonance magnitude around the fundamental mode and the lowest overtones can cross the real axis into the unstable regime of the complex plane, unveiling the existence of nonmodal pseudo-resonances. A pseudospectrum analysis further predicts that fluctuations to the system may destabilize the object when next to leading-order effects are considered, as the triggering of pseudo-resonant growth can break the order-expansion of black-hole perturbation theory.

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arXiv2023

Building post-Newtonian neutron stars

Owed to their compactness, neutron stars involve strong gravity and extreme density physics. Nevertheless, at present, there are a variety of problems where progress (at least conceptually) can be made in the context of weak gravity. Motivated by this we examine how accurately one can model neutron stars using the post-Newtonian approximation to general relativity. In general, we find there is a significant degree of freedom in how the post-Newtonian equations of stellar structure can be formulated. We discuss this flexibility in the formulation and provide examples to demonstrate the impact on stellar models. We also consider the (closely related) problem of building neutron stars using isotropic coordinates. In this context, we provide a new strategy for solving the equations (based on a scaling argument) which significantly simplifies the problem.

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arXiv2022

Gravitational waves from extreme-mass-ratio systems in astrophysical environments

We establish a generic, fully-relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically-symmetric, non-vacuum black-hole spacetimes. The potential applications to astrophysical setups range from black holes accreting baryonic matter to those within axionic clouds and dark matter environments, allowing to assess the impact of the galactic potential, of accretion, gravitational drag and halo feedback on the generation and propagation of gravitational-waves. We apply our methods to a black hole within a halo of matter. We find fluid modes imparted to the gravitational-wave signal (a clear evidence of the black hole fundamental mode instability) and the tantalizing possibility to infer galactic properties from gravitational-wave measurements by sensitive, low-frequency detectors.

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arXiv2022

Conservative Evolution of Black Hole Perturbations with Time-Symmetric Numerical Methods

The scheduled launch of the LISA Mission in the next decade has called attention to the gravitational self-force problem. Despite an extensive body of theoretical work, long-time numerical computations of gravitational waves from extreme-mass-ratio-inspirals remain challenging. This work proposes a class of numerical evolution schemes suitable to this problem based on Hermite integration. Their most important feature is time-reversal symmetry and unconditional stability, which enables these methods to preserve symplectic structure, energy, momentum and other Noether charges over long time periods. We apply Noether's theorem to the master fields of black hole perturbation theory on a hyperboloidal slice of Schwarzschild spacetime to show that there exist constants of evolution that numerical simulations must preserve. We demonstrate that time-symmetric integration schemes based on a 2-point Taylor expansion (such as Hermite integration) numerically conserve these quantities, unlike schemes based on a 1-point Taylor expansion (such as Runge-Kutta). This makes time-symmetric schemes ideal for long-time EMRI simulations.

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arXiv2022

The Maxwell-scalar field system near spatial infinity

We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions which depend on the coupling constant between the Maxwell and scalar fields. We analyse the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.

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arXiv2022

Hyperboloidal method for frequency-domain self-force calculations

Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and the order of the perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, and (iii) unbounded support. The latter, in particular, is important for emerging second-order (in the mass ratio) calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on standard time slices with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behavior. This approach has been very successful, but the boundary conditions calculations are tedious, and the approach is not well suited to unbounded sources where homogeneous solutions must be computed at all radii. This work develops an alternative approach where hyperboloidal slices foliate the spacetime, and compactifying coordinates simplify the boundary treatment. We implement this approach with a multi-domain spectral solver with analytic mesh refinement and use the scalar-field self-force on circular orbits around a Schwarzschild black hole as an example problem. The method works efficiently for all three source classes encountered in self-force calculations and has distinct advantages over the traditional approach. For example, our code efficiently computes the perturbation for orbits with extremely large orbital radii ($r_{p}>10^5M$) or modes with very high spherical harmonic mode index ($\ell \ge 100$). Our results indicate that hyperboloidal methods can play an essential role in self-force calculations.

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arXiv2022

Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea

Recent work applying the notion of pseudospectrum to gravitational physics showed that the quasinormal mode spectrum of black holes is unstable, with the possible exception of the longest-lived (fundamental) mode. The fundamental mode dominates the expected signal in gravitational wave astronomy, and there is no reason why it should have privileged status. We compute the quasinormal mode spectrum of two model problems where the Schwarzschild potential is perturbed by a small "bump" consisting of either a Pöschl-Teller potential or a Gaussian, and we show that the fundamental mode is destabilized under generic perturbations. We present phase diagrams and study a simple double-barrier toy problem to clarify the conditions under which the spectral instability occurs.

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