arXiv subjects

Sebastian H. Völkel

Publications and source records attributed to Sebastian H. Völkel.

At least 37 records · Page 2Linked to original sources

arXiv2024

Higher-derivative corrections to the Kerr quasinormal mode spectrum

We provide the most complete analysis so far of quasinormal modes of rotating black holes in a general higher-derivative extension of Einstein's theory. By finding the corrections to the Teukolsky equation and expressing them in a simple form, we are able to apply a generalized continued fraction method that allows us to find the quasinormal mode frequencies including overtones. We obtain the leading-order corrections to the Kerr quasinormal mode frequencies of all the $(l,m,n)$ modes with $l=2,3,4$, $-l\le m\le l$ and $n=0,1,2$, and express them as a function of the black hole spin $χ$ using polynomial fits. We estimate that our results remain accurate up to spins between $χ\sim 0.7$ and $χ\sim 0.95$, depending on the mode. We report that overtones are overall more sensitive to corrections, which is expected from recent literature on this topic. We also discuss the limit of validity of the linear corrections to the quasinormal mode frequencies by estimating the size of nonlinear effects in the higher-derivative couplings. All our results are publicly available in an online repository.

gr-qc↗

arXiv2024

Inverse problem in energy-dependent potentials using semiclassical methods

Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials.

hep-ph↗

arXiv2024

Inverse problem of analog gravity systems

Analog gravity models of black holes and exotic compact objects provide a unique opportunity to study key properties of such systems in controlled laboratory environments. In contrast to astrophysical systems, analog gravity systems can be prepared carefully and their dynamical aspects thus investigated in unprecedented ways. While gravitational wave scattering properties of astrophysical compact objects are more connected to quasinormal modes, laboratory experiments can also access the transmission and reflection coefficients, which are otherwise mostly relevant for Hawking radiation related phenomena. In this work, we report two distinct results. First, we outline a semiclassical, nonparametric method that allows for the reconstruction of the effective perturbation potential from the knowledge of transmission and reflection coefficients for certain types of potentials in the Schrödinger wave equation admitting resonant tunneling. Second, we show how to use our method by applying it to an imperfect draining vortex, which has been suggested as an analog of extreme compact objects. Although the inverse problem is, in general, not unique, choosing physically motivated assumptions and requiring the validity of semiclassical theory, we demonstrate that the method provides efficient and accurate results.

gr-qc↗

arXiv2024

Rapidly rotating neutron stars: Universal relations and EOS inference

We provide accurate universal relations that allow to estimate the moment of inertia $I$ and the ratio of kinetic to gravitational binding energy $T/W$ of uniformly rotating neutron stars from the knowledge of mass, radius, and moment of inertia of an associated non-rotating neutron star. Based on these, several other fluid quantities can be estimated as well. Astrophysical neutron stars rotate to varying degrees, and, although rotational effects may be neglected in some cases, not modeling them will inevitably introduce bias when performing parameter estimation. This is especially important for future, high-precision measurements coming from electromagnetic and gravitational wave observations. The proposed universal relations facilitate computationally cheap EOS inference codes that permit the inclusion of observations of rotating neutron stars. To demonstrate this, we deploy them into a recent Bayesian framework for equation of state parameter estimation that is now valid for arbitrary, uniform rotation. Our inference results are robust up to around percent level precision for the generated neutron star observations, consisting of the mass, equatorial radius, rotation rate, as well as co- and counter-rotating $f$-mode frequencies, that enter the framework as data.

gr-qc↗

arXiv2023

A parametrized quasi-normal mode framework for non-Schwarzschild metrics

In this work we comment in more detail on what happens to the parametrized framework first presented by Cardoso et al. when there are departures from the Schwarzschild background metric, as well as possible deviations in the "dynamics". We treat possible deviations in the background metric with additional coefficients with respect to the original works. The advantages of this reformulation are clear when applied to a parameter estimation problem, since the coefficients are always real, and many of them do not depend on the overtone number and angular momentum of the frequency, thus eventually reducing the total amount of parameters to be inferred.

gr-qc↗

arXiv2023

Quasi-normal modes of non-separable perturbation equations: the scalar non-Kerr case

Scalar, vector and tensor perturbations on the Kerr spacetime are governed by equations that can be solved by separation of variables, but the same is not true in generic stationary and axisymmetric geometries. This complicates the calculation of black-hole quasi-normal mode frequencies in theories that extend/modify general relativity, because one generally has to calculate the eigenvalue spectrum of a two-dimensional partial differential equation (in the radial and angular variables) instead of an ordinary differential equation (in the radial variable). In this work, we show that if the background geometry is close to the Kerr one, the problem considerably simplifies. One can indeed compute the quasi-normal mode frequencies, at least at leading order in the deviation from Kerr, by solving an ordinary differential equation subject to suitable boundary conditions. Although our method is general, in this paper we apply it to scalar perturbations on top of a Kerr black hole with an anomalous quadrupole moment, or on top of a slowly rotating Kerr background.

gr-qc↗

arXiv2023

Role of black hole quasinormal mode overtones for ringdown analysis

Extracting quasinormal modes from compact binary mergers to perform black hole spectroscopy is one of the fundamental pillars in current and future strong-gravity tests. Among the most remarkable findings of recent works is that including a large number of overtones not only reduces the mismatch of the fitted ringdown but also allows one to extract black hole parameters from a ringdown analysis that goes well within the nonlinear merger part. At the same time, it is well understood that several details of the ringdown analysis have important consequences for the question of whether overtones are present or not, and subsequently, to what extent one can claim to perform black hole spectroscopy. To clarify and tackle some aspects of overtone fitting, we revisit the clearer problem of wave propagation in the scalar Regge-Wheeler and Pöschl-Teller potentials. This setup, which is to some extent qualitatively very similar to the nonlinear merger-ringdown regime, indicates that using even an approximate model for the overtones yields an improved extraction of the black hole mass at early ringdown times. We find that the relevant parameter is the number of included modes rather than using the correct model for the overtones themselves. These results show that some standard tests for verifying the physical contribution of an overtone to a waveform can be misleading, and that even in the linear case it can be difficult to distinguish the presence of an excited mode from the fitting of non-QNM effects.

gr-qc↗

arXiv2023

Quasi-Normal Modes from Bound States: The Numerical Approach

It is known that the spectrum of quasi-normal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasi-normal modes, but it is limited to a few "approximate" potentials with certain transformation properties for which the spectrum of bound states must be known analytically. In this work we circumvent this limitation by proposing an approach that allows one to make use of potentials with similar transformation properties, but where the spectrum of bound states can also be computed numerically. Because the numerical calculation of bound states is usually more stable than the direct computation of the corresponding quasi-normal modes, the new approach is also interesting from a technical point of view. We apply the method to different potentials, including the Pöschl-Teller potential for which all steps can be understood analytically, as well as potentials for which we are not aware of analytic results but provide independent numerical results for comparison. As a canonical test, all potentials are chosen to match the Regge-Wheeler potential of axial perturbations of the Schwarzschild black hole. We find that the new approximate potentials are more suitable to approximate the exact quasi-normal modes than the Pöschl-Teller potential, particularly for the first overtone. We hope this work opens new perspectives to the computation of quasi-normal modes and finds further improvements and generalizations in the future.

gr-qc↗

arXiv2023

Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes

In modified theories of gravity, the potentials appearing in the Schrödinger-like equations that describe perturbations of non-rotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole's quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain-Monte-Carlo (MCMC) methods to recover the coefficients in the $M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time, and in a ``pessimistic'' scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole `shadows'' by the Event Horizon Telescope and future instruments.

gr-qc↗

arXiv2023

Testing General Relativity with Black Hole Quasi-Normal Modes

The purpose of this chapter is to provide an overview of the exciting field of black hole quasi-normal modes and its capabilities to test general relativity in the 21st century. After motivating this line of research, we provide a qualitative introduction to the concept of quasi-normal modes and outline black hole perturbation theory. With the perturbation equations at hand, we discuss common methods to compute the quasi-normal mode spectrum and compare the advantages and disadvantages of each approach. We also provide an overview of possible deviations from general relativity and how they modify the quasi-normal mode spectrum of black holes from a theoretical point of view. We then review the rapidly evolving status of currently operating gravitational wave observatories and experimental results. The chapter concludes with a discussion of open problems and promising outlooks to theoretical and experimental developments. Central pieces that make this chapter particularly interesting, also for advanced readers, are comprehensive tables providing a detailed overview of the status of techniques to compute quasi-normal modes and methods to describe quasi-normal modes of rotating black holes beyond general relativity.

gr-qc↗

arXiv2022

Constraining the Nuclear Equation of State from Rotating Neutron Stars

We demonstrate how observables of slowly rotating neutron stars can be used to constrain the nuclear equation of state. By building a Bayesian framework we demonstrate how combining different types of neutron star measurements, motivated by the upcoming multi-messenger era, provide informative posterior distributions of commonly used equation of state parametrizations. Exemplarily, we chose the Read et al. four parameter model that is widely used to represent realistic equations of states in neutron star physics. Since future observational campaigns will not only provide mass, radius and rotation rate measurements, but also neutron star oscillation modes, a unified framework to analyze the joint knowledge becomes necessary. While several attempts exist in the literature, the here presented framework explicitly takes into account rotational effects by using state-of-the-art universal relations for their oscillation spectra. To demonstrate its performance we apply it to observables that take into account rotational effects to best possible precision and use our independent model for the reconstruction. Only a few high precision neutron star measurements are required to put tight constraints on the underlying equation of state.

gr-qc↗

arXiv2022

Theory-agnostic Reconstruction of Potential and Couplings from Quasi-Normal Modes

In this work, we use a parametrized theory-agnostic approach that connects the observation of black hole quasi-normal modes with the underlying perturbation equations, with the goal of reconstructing the potential and the coupling functions appearing in the latter. The fundamental quasi-normal mode frequency and its first two overtones are modeled through a second order expansion in the deviations from general relativity, which are assumed to be small but otherwise generic. By using a principal component analysis, we demonstrate that percent-level measurements of the fundamental mode and its overtones can be used to constrain the effective potential of tensor perturbations and the coupling functions between tensor modes and ones of different helicity, without assuming an underlying theory. We also apply our theory-agnostic reconstruction framework to analyze simulated quasi-normal mode data produced within specific theories extending general relativity, such as Chern-Simons gravity.

gr-qc↗

arXiv2022

On Black Hole Area Quantization and Echoes

In this work we argue that black hole area quantization of Bekenstein and Mukhanov should not give rise to measurable effects in terms of so-called gravitational wave echoes during black hole mergers. We outline that the quantum spectrum of a black hole should be washed out during and after black hole mergers, and hence one should not expect echoes in this scenario. The extreme broadening of the spectrum is due to the large particle emission rate during ringdown. Our results question key assumptions being made in recent literature on this topic.

gr-qc↗

arXiv2021

Separating Astrophysics and Geometry in Black Hole Images

The observation of the shadow of the supermassive black hole M87$^{*}$ by the Event Horizon Telescope (EHT) is sensitive to the spacetime geometry near the circular photon orbit and beyond, and it thus has the potential to test general relativity in the strong field regime. Obstacles to this program, however, include degeneracies between putative deviations from general relativity and both the description of the accretion flow and the uncertainties on "calibration parameters", such as e.g. the mass and spin of the black hole. In this work, we introduce a formalism, based on a principal component analysis, capable of reconstructing the black hole metric (i.e. the "signal") in an agnostic way, while subtracting the "foreground" due to the uncertainties in the calibration parameters and the modelling of the accretion flow. We apply our technique to simulated mock data for spherically symmetric black holes surrounded by a thick accretion disk. We show that separation of signal and foreground may be possible with next generation EHT-like experiments.

gr-qc↗

arXiv2021

EHT tests of the strong-field regime of General Relativity

Following up on a recent analysis by Psaltis et al. [Phys. Rev. Lett. 125, 141104 (2020)], we show that the observed shadow size of M87$^*$ can be used to unambiguously and robustly constrain the black hole geometry in the vicinity of the circular photon orbit. Constraints on the post-Newtonian weak-field expansion of the black hole's metric are instead more subtle to obtain and interpret, as they rely on combining the shadow-size measurement with suitable theoretical priors. We provide examples showing that post-Newtonian constraints resulting from shadow-size measurements should be handled with extreme care. We also discuss the similarities and complementarity between the EHT shadow measurements and black-hole gravitational quasi-normal modes.

gr-qc↗

arXiv2021

Fast Rotating Neutron Stars: Oscillations and Instabilities

In this review article, we present the main results from our most recent research concerning the oscillations of fast rotating neutron stars. We derive a set of time evolution equations for the investigation of non-axisymmetric oscillations of rapidly rotating compact objects in full general relativity, taking into account the contribution of a dynamic spacetime. Using our code, which features high accuracy at comparably low computational expense, we are able to extract the frequencies of non-axisymmetric modes of compact objects with rotation rates up to the Kepler limit. We propose various universal relations combining bulk properties of isolated neutron stars as well as of binary systems before and after merger; these relations are independent of the true equation of state and may serve as a valuable tool for gravitational wave asteroseismology. We also present an introductory example using a Bayesian analysis.

gr-qc↗

arXiv2021

Bayesian Inverse Problem of Rotating Neutron Stars

In this work we provide a framework that connects the co-rotating and counter rotating $f$-mode frequencies of rotating neutron stars with their stellar structure. The accurate computation of these modes for realistic equations of state has been presented recently and they are here used as input for a Bayesian analysis of the inverse problem. This allows to quantitatively reconstruct basic neutron star parameters, such as the mass, radius, rotation rate or universal scaling parameters. We find that future observations of both $f$-mode frequencies, in combination with a Bayesian analysis, would provide a promising direction to solve the inverse stellar problem. We provide two complementary approaches, one that is equation of state dependent and one that only uses universal scaling relations. We discuss advantages and disadvantages of each approach, such as possible bias and robustness. The focus is on astrophysically motivated scenarios in which informed prior information on the neutron star mass or rotation rate can be provided and study how they impact the results.

gr-qc↗

arXiv2021

Exact theory for the Rezzolla-Zhidenko metric and self-consistent calculation of quasinormal modes

A covariant, scalar-tensor gravity is constructed such that the static, spherically symmetric Rezzolla-Zhidenko metric is an exact solution to the theory. The equations describing gravitational perturbations of this spacetime, which represents a generic black hole possessing an arbitrary number of hairs, can then be derived. This allows for a self-consistent study of the associated quasinormal modes. It is shown that mode spectra are tied to not only the non-Einstein parameters in the metric but also to those that appear at the level of the action, and that different branches of the exact theory can, in some cases, predict significantly different oscillation frequencies and damping times. For choices which make the theory appear more like general relativity in some precise sense, we find that a nontrivial Rezzolla-Zhidenko parameter space is permissible under current constraints on fundamental ringdown modes observed by Advanced LIGO.

gr-qc↗