arXiv subjects

Rodrigo Panosso Macedo

Publications and source records attributed to Rodrigo Panosso Macedo.

49 records · Page 3Linked to original sources

arXiv2022

Black holes in galaxies: environmental impact on gravitational-wave generation and propagation

We introduce a family of solutions of Einstein's gravity minimally coupled to an anisotropic fluid, describing asymptotically flat black holes with "hair" and a regular horizon. These spacetimes can describe the geometry of galaxies harboring supermassive black holes, and are extensions of Einstein clusters to include horizons. They are useful to constrain the environment surrounding astrophysical black holes, using electromagnetic or gravitational-wave observations. We compute the main properties of the geometry, including the corrections to the ringdown stage induced by the external matter and fluxes by orbiting particles. The leading order effect to these corrections is a gravitational-redshift, but gravitational-wave propagation is affected by the galactic potential in a nontrivial way, and may be characterized with future observatories.

gr-qc↗

arXiv2021

Pseudospectrum of Reissner-Nordström black holes: quasinormal mode instability and universality

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, so it is critical to understand if the quasinormal mode spectrum is stable against perturbations. It was recently shown that the pseudospectrum can shed light on the spectral stability of black hole quasinormal modes. We study the pseudospectrum of Reissner-Nordström spacetimes and we find a spectral instability of scalar and gravitoelectric quasinormal modes in subextremal and extremal black holes, extending similar findings for the Schwarzschild spacetime. The asymptotic structure of pseudospectral contour levels is the same for scalar and gravitoelectric perturbations. By making different gauge choices in the hyperboloidal slicing of the spacetime, we find that the broad features of the pseudospectra are remarkably gauge-independent. The gravitational-led and electromagnetic-led quasinormal modes of extremal Reissner-Nordström black holes exhibit "strong" isospectrality: not only their spectrum coincides, but the whole pseudospectrum is the same for both classes of perturbations. We observe that a conformal duality between the extremal horizon and spacetime boundaries at infinity is responsible for such "strong" isospectrality property.

gr-qc↗

arXiv2021

Gravitational wave signatures of black hole quasi-normal mode instability

Black hole (BH) spectroscopy has emerged as a powerful approach to extract spacetime information from gravitational wave (GW) observed signals. Yet, quasinormal mode (QNM) spectral instability under high wave-number perturbations has been recently shown to be a common classical general relativistic phenomenon [1]. This requires to assess its impact on the BH QNM spectrum, in particular on BH QNM overtone frequencies. We conclude: i) perturbed BH QNM overtones are indeed potentially observable in the GW waveform, providing information on small-scale environment BH physics, and ii) their detection poses a challenging data analysis problem of singular interest for LISA astrophysics. We adopt a two-fold approach, combining theoretical results from scattering theory with a fine-tuned data analysis on a highly-accurate numerical GW ringdown signal. The former introduces a set of effective parameters (partially lying on a BH Weyl law) to characterise QNM instability physics. The latter provides a proof-of-principle demonstrating that the QNM spectral instability is indeed accessible in the time-domain GW waveform, though certainly requiring large signal-to-noise ratios. Particular attention is devoted to discuss the patterns of isospectrality loss under QNM instability, since the disentanglement between axial and polar GW parities may already occur within the near-future detection range.

gr-qc↗

arXiv2021

Pseudospectrum and black hole quasi-normal mode (in)stability

We study the stability of quasinormal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals the following: (i) the stability of the slowest-decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert [H. P. Nollert, About the Significance of Quasinormal Modes of Black Holes, Phys. Rev. D 53, 4397 (1996)] as an "infrared" effect; (ii) the instability of all overtones under small-scale ("ultraviolet") perturbations of sufficiently high frequency, which migrate towards universal QNM branches along pseudospectra boundaries, shedding light on Nollert's pioneer work and Nollert and Price's analysis [H. P. Nollert and R. H. Price, Quantifying Excitations of Quasinormal Mode Systems, J. Math. Phys. (N.Y.) 40, 980 (1999)]. Methodologically, a compactified hyperboloidal approach to QNMs is adopted to cast QNMs in terms of the spectral problem of a non-self-adjoint operator. In this setting, spectral (in)stability is naturally addressed through the pseudospectrum notion that we construct numerically via Chebyshev spectral methods and foster in gravitational physics. After illustrating the approach with the Pöschl-Teller potential, we address the Schwarzschild black hole case, where QNM (in)stabilities are physically relevant in the context of black hole spectroscopy in gravitational-wave physics and, conceivably, as probes into fundamental high-frequency spacetime fluctuations at the Planck scale.

gr-qc↗

arXiv2021

Fully pseudospectral solution of the conformally invariant wave equation on a Kerr background

We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately represented as a cylinder. Earlier studies of the wave equation on a Schwarzschild background have revealed important details about the regularity of the corresponding solutions. It was found that, on the cylinder, the solutions generically develop logarithmic singularities at infinitely many orders. Moreover, these singularities also `spread' to future null infinity. However, by imposing certain regularity conditions on the initial data, the lowest-order singularities can be removed. Here we are interested in a generalisation of these results to a rotating black hole background and study the influence of the rotation rate on the properties of the solutions. To this aim, we first construct a conformal compactification of the Kerr solution which yields a suitable representation of the cylinder at spatial infinity. Besides analytical investigations on the cylinder, we numerically solve the wave equation with a fully pseudospectral method, which allows us to obtain highly accurate numerical solutions. This is crucial for a detailed analysis of the regularity of the solutions. In the Schwarzschild case, the numerical problem could effectively be reduced to solving $(1+1)$-dimensional equations. Here we present a code that can perform the full $2+1$ evolution as required for axisymmetric waves on a Kerr background.

gr-qc↗

arXiv2020

Hyperboloidal framework for the Kerr spacetime

Motivated by the need of a robust geometrical framework for the calculation of long, and highly accurate waveforms for extreme-mass-ratio inspirals, this work presents an extensive study of the hyperboloidal formalism for the Kerr spacetime and the Teukolsky equation. In a first step, we introduce a generic coordinate system foliating the Kerr spacetime into hypersurfaces of constant time extending between the black-hole horizon and future null infinity, while keeping track of the underlying degrees of freedom. Then, we express the Teukolsky equation in terms of these generic coordinates with focus on applications in both the time and frequency domains. Specifically, we derive a wave-like equation in $2+1$ dimensions, whose unique solution follows directly from the prescription of initial data (no external boundary conditions). Moreover, we extend the hyperboloidal formulation into the frequency domain. A comparison with the standard form of the Teukolsky equations allows us to express the regularisation factors in terms of the hyperboloidal degrees of freedom. In the second part, we discuss several hyperboloidal gauges for the Kerr solution. Of particular importance, this paper introduces the minimal gauge. The resulting expressions for the Kerr metric and underlying equations are simple enough for eventual (semi)-analytical studies. Despite the simplicity, the gauge has a very rich structure as it naturally leads to two possible limits to extremality, namely the standard extremal Kerr spacetime and its near-horizon geometry. When applied to the Teukolsky equation in the frequency domain, we show that the minimal gauge actually provides the spacetime counterpart of the well-known Leaver's formalism. Finally, we recast the hyperboloidal gauges for the Kerr spacetime available in the literature within the framework introduced here.

gr-qc↗

arXiv2019

End point of nonaxisymmetric black hole instabilities in higher dimensions

We report on the end state of nonaxisymmetric instabilities of singly spinning asymptotically flat Myers-Perry black holes. Starting from a singly spinning black hole in D=5,6,7 dimensions, we introduce perturbations with angular dependence described by m=2, m=3, or m=4 azimuthal mode numbers about the axis of rotation. In D=5, we find that all singly spinning Myers-Perry black holes are stable, in agreement with the results from perturbation theory. In D=6 and 7, we find that these black holes are nonlinearly stable only for sufficiently low spins. For intermediate spins, although the m=2 bar mode becomes unstable and leads to large deformations, the black hole settles back down to another member of the Myers-Perry family via gravitational wave emission; surprisingly, we find that all such unstable black holes settle to the same member of the Myers-Perry family. The amount of energy radiated into gravitational waves can be very large, in some cases more than 30% of the initial total mass of the system. For high enough spins, the m=4 mode becomes the dominant unstable mode, leading to deformed black holes that develop local Gregory-Laflamme instabilities, thus forming a naked singularity in finite time, which is further evidence for the violation of the weak cosmic censorship conjecture in asymptotically flat higher-dimensional spacetimes.

hep-th↗

arXiv2019

Comment on "Some exact quasinormal frequencies of a massless scalar field in Schwarzschild spacetime"

A new branch of quasinormal modes for a massless scalar field propagating on the Schwarzschild spacetime was recently announced [1807.04513]. We review the quasinormal modes characterisation and arguments and identify the flaws in their proof. Then, we preset explicit counterexamples to such arguments. Finally, we study the modes via alternative methods and do not find the new branch. We conclude against their interpretation.

gr-qc↗

arXiv2018

Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordström case

We study quasi-normal modes of black holes, with a focus on resonant (or quasi-normal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild in this geometric approach to spherically symmetric asymptotically flat black hole spacetimes, in particular Reissner-Nordström. The discussion involves, first, the non-trivial technical developments needed to address the choice of appropriate hyperboloidal slices in the extended setting as well as the generalization of the algorithm determining the coefficients in the expansion of the solution in terms of the quasi-normal modes. In a second stage, we discuss how the adopted framework provides a geometric insight into the origin of regularization factors needed in Leaver's Cauchy based foliations, as well as into the discussion of quasi-normal modes in the extremal black hole limit.

gr-qc↗

arXiv2016

Gyromagnetic factor of rotating disks of electrically charged dust in general relativity

We calculated the dimensionless gyromagnetic ratio ("$g$-factor") of self-gravitating, uniformly rotating disks of dust with a constant specific charge $ε$. These disk solutions to the Einstein-Maxwell equations depend on $ε$ and a "relativity parameter" $γ$ ($0<γ\le 1$) up to a scaling parameter. Accordingly, the $g$-factor is a function $g=g(γ,ε)$. The Newtonian limit is characterized by $γ\ll 1$, whereas $γ\to 1$ leads to a black-hole limit. The $g$-factor, for all $ε$, approaches the values $g=1$ as $γ\to 0$ and $g=2$ as $γ\to 1$.

gr-qc↗

arXiv2016

Spectral decomposition of black-hole perturbations on hyperboloidal slices

In this paper we present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschild-black-hole background. The wave equa- tion in question is Laplace-transformed which leads to a spatial differential equation with a complex parameter. For initial data which are analytic with respect to a compactified spatial coordinate, this equation is treated with the help of the Mathematica-package in terms of a sophisticated Taylor series analysis. Thereby, all ingredients of the desired spectral decomposition arise explicitly to arbitrarily prescribed accuracy, including quasi normal modes, quasi normal mode amplitudes as well as the jump of the Laplace-transform along the branch cut. Finally, all contributions are put together to obtain via the inverse Laplace transformation the spectral de- composition in question. The paper explains extensively this procedure and includes detailed discussions of relevant aspects, such as the definition of quasi normal modes and the question regarding the contribution of infinity frequencies modes to the early time response of the black hole.

gr-qc↗

arXiv2014

Initial data for perturbed Kerr black holes on hyperboloidal slices

We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal ("ACMC-") slices on which the mean extrinsic curvature K asymptotically approaches a constant at future null infinity scri+. More precisely, we require that K obeys the Taylor expansion K=K0 + s^4 where K0 is a constant and s describes a compactified spatial coordinate such that scri+ is represented by s=0. We excise the singular interior of the black hole and assume a marginally outer trapped surface as inner boundary of the computational domain. The momentum and Hamiltonian constraints are solved by means of pseudo-spectral methods and we find exponential rates of convergence of our numerical solutions. Some physical properties of the initial data are studied with the calculation of the Bondi Mass, together with a multipole decomposition of the horizon. We probe the standard picture of gravitational collapse by assessing a family of Penrose-like inequalities and discuss in particular their rigidity aspects. Dynamical evolutions are planned in a future project.

gr-qc↗

arXiv2014

Axisymmetric constant mean curvature slices in the Kerr space-time

Recently, there have been efforts to solve Einstein's equation in the context of a conformal compactification of space-time. Of particular importance in this regard are the so called CMC-foliations, characterized by spatial hyperboloidal hypersurfaces with a constant extrinsic mean curvature K. However, although of interest for general space-times, CMC-slices are known explicitly only for the spherically symmetric Schwarzschild metric. This work is devoted to numerically determining axisymmetric CMC-slices within the Kerr solution. We construct such slices outside the black hole horizon through an appropriate coordinate transformation in which an unknown auxiliary function A is involved. The condition K=const. throughout the slice leads to a nonlinear partial differential equation for the function A, which is solved with a pseudo-spectral method. The results exhibit exponential convergence, as is to be expected in a pseudo-spectral scheme for analytic solutions. As a by-product, we identify CMC-slices of the Schwarzschild solution which are not spherically symmetric.

gr-qc↗