arXiv subjects

Sebastian H. Völkel

Publications and source records attributed to Sebastian H. Völkel.

45 records · Page 3Linked to original sources

arXiv2020

Bayesian Metric Reconstruction with Gravitational Wave Observations

Theories of gravity extending or modifying general relativity typically allow for black hole solutions different from the Schwarzschild/Kerr geometries. Electromagnetic observations have been used to place constraints on parametrized deviations from the Schwarzschild/Kerr metrics, in an effort to gain insight on the underlying gravitational theory. In this work, we show that observations of the gravitational quasi-normal modes by existing and future interferometers can be used to bound the same parametrized black hole metrics that are constrained by electromagnetic observations (e.g. by the Event Horizon Telescope). We argue that our technique is most sensitive to changes in the background black hole metric near the circular photon orbit, and that it is robust against the changes that a gravitational theory differing from general relativity necessarily introduces in the equations for the gravitational perturbations. We demonstrate our approach by reconstructing the background metric from a set of simulated observations using a Bayesian approach.

gr-qc↗

arXiv2019

Spectral Lines of Quantized, Spinning Black Holes and their Astrophysical Relevance

In this Letter, we study black hole area quantization in the context of gravitational wave physics. It was recently argued that black hole area quantization could be a mechanism to produce so-called echoes as well as characteristic absorption lines in gravitational wave observations of merging black holes. One can match the spontaneous decay of these quantum black holes to Hawking radiation calculations. Using some assumptions, one can then estimate the natural widths of these states. As can be seen from a classical paper by Bekenstein and Mukhanov, the ratio between width and spacing of nonspinning black hole states approaches a small constant, which seems to confirm the claim. However, we find that, including the effect of black hole spin, the natural widths increase. To properly address any claim about astrophysical black holes, one should examine the spinning case, as real black holes spin. Thus, the word spinning is key to the question of whether or not black holes should have an observable spectrum in nature. Our results suggest that it should be possible to distinguish between any scenarios for which the answer to this question is yes. However, for all of the commonly discussed scenarios, our answer is almost certainly no.

gr-qc↗

arXiv2019

Scalar Fields and Parametrized Spherically Symmetric Black Holes: Can one hear the shape of space-time?

In this work we study whether parametrized spherically symmetric black hole solutions in metric theories of gravity can appear to be isospectral when studying perturbations. From a theory agnostic point of view, the test scalar field wave equation is the ideal starting point to approach the quasi-normal mode spectrum in alternative black hole solutions. We use a parametrization for the metric proposed by Rezzolla and Zhidenko, as well as the the higher order WKB method in the determination of the quasi-normal mode spectra. We look for possible degeneracies in a tractable subset of the parameter space with respect to the Schwarzschild quasi-normal modes. Considering the frequencies and damping times of the expected observationally most relevant quasi-normal modes, we find such degeneracies. We explicitly demonstrate that the leading Schwarzschild quasi-normal modes can be approximated by alternative black hole solutions when their mass is treated as free parameter. In practice, we conclude that the mass has to be known with extremely high precision in order to restrict the leading terms in the metric expansion to currently known limits coming from the PPN expansion. Possible limitations of using the quasi-normal mode ringdown to investigate black hole space-times are being discussed.

gr-qc↗

arXiv2019

The Inverse Problem for Hawking Radiation

In this work we study the inverse problem related to the emission of Hawking radiation. We first show how the knowledge of greybody factors of different angular contributions $l$ can be used to constrain the width of the corresponding black hole perturbation potentials. Afterwards we provide a framework to recover the greybody factors from the actual energy emission spectrum, which has to be treated as sum over all multipole numbers. The underlying method for the reconstruction of the potential widths is based on the inversion of the Gamow formula, a parabolic expansion and the Pöschl-Teller potential. We define a `normalized' energy emission spectrum that turns out to be very beneficial for the numerical fitting process, as well as for an improved qualitative understanding of how much information of the black hole potentials are actually imprinted in the spectrum. The connection to recent studies on the inverse problem using the quasi-normal spectra of ultra compact stars and exotic compact objects is discussed as well. In the appendix we show that the spectrum can be approximated surprisingly well and simply with a parabolic expansion of the peak of the classical black hole scattering potentials.

gr-qc↗

arXiv2019

On the Inverse Spectrum Problem of Neutron Stars

In this work we revisit axial perturbations of spherically symmetric and non-rotating neutron stars. Although it has been object of many studies, it still offers new insights that are of potential interest for more realistic scenarios or in the study exotic compact objects, which have drawn much attention recently. By using WKB theory, we first derive a new Bohr-Sommerfeld rule that allows to investigate the quasi-normal mode spectrum and address the inverse spectrum problem. The pure analytical treatment of the wave equation is rather involved, because it requires the solution of the TOV equations and the non-trivial tortoise coordinate transformation depending on the underlying space-time. Therefore we provide an easy way to construct potentials that simplifies the analytical treatment, but still captures the relevant physics. The approximated potential can be used for calculations of the axial perturbation spectrum. These results are also useful in the treatment of the inverse problem. We demonstrate this by reconstructing the time-time component of the metric throughout the star and constraining the equation of state in the central region. Our method also provides an analytical explanation of the empirically known asteroseismology relation that connects the fundamental QNM and radius of a neutron star with its compactness.

gr-qc↗

arXiv2018

Wormhole Potentials and Throats from Quasi-Normal Modes

Exotic compact objects refer to a wide class of black hole alternatives or effective models to describe phenomenologically quantum gravitational effects on the horizon scale. In this work we show how the knowledge of the quasi-normal mode spectrum of non-rotating wormhole models can be used to reconstruct the effective potential that appears in the perturbation equations. From this it is further possible to obtain the parameters that characterize the specific wormhole model, which in this paper was chosen to be the one by Damour and Solodukhin. We also address the question whether one can distinguish such type of wormholes from ultra compact stars, if only the quasi-normal mode spectrum is known. We have proven that this is not possible by using the trapped modes only, but requires additional information. The here presented inverse method is an extension of work that has previously been developed and applied to the oscillation spectra of ultra compact stars and gravastars. However, it is not limited to the study of exotic compact objects, but applicable to symmetric double barrier potentials that appear in one-dimensional wave equations. Therefore we think it can be of interest for other fields too.

gr-qc↗

arXiv2018

Inverse spectrum problem for quasi-stationary states

In this work we present a semi-classical approach to solve the inverse spectrum problem for one-dimensional wave equations for a specific class of potentials that admits quasi-stationary states. We show how inverse methods for potential wells and potential barriers can be generalized to reconstruct significant parts for the combined potentials. For the reconstruction one assumes the knowledge of the complex valued spectrum and uses the exponential smallness of its imaginary part. Analytic spectra are studied and a recent application of the method in the literature for gravitational wave physics is discussed. The method allows for a simple reconstruction of quasi-stationary state potentials from a given spectrum. Thus it might be interesting for different branches of physics and related fields.

quant-ph↗

arXiv2017

Ultra Compact Stars: Reconstructing the Perturbation Potential

In this work we demonstrate how different semi-classical methods can be combined in a novel way to reconstruct the perturbation potential of ultra compact stars. Besides rather general assumptions, the only specific information entering this approach is the spectrum of the $\textit{trapped}$ axial quasi-normal modes. In general it is not possible to find a unique solution for the potential in the inverse problem, but instead a family of potentials producing the same spectrum. Nevertheless, this already determines important properties of the involved potential and can be used to rule out many candidate models. A unique solution was found based on the additional natural assumption that the exterior part ($r \gtrsim 3\,M$) is described by the Regge-Wheeler potential. This is true in general relativity for any non-rotating spherically symmetric object. This technique can be potentially applied for the study of deviations from general relativity. The methods we demonstrate are easy to implement and rather general, therefore we expect them also to be interesting for other fields where inverse spectrum problems are studied, e.g. quantum physics and molecular spectroscopy.

gr-qc↗

arXiv2017

A Semi-analytic Study of Axial Perturbations of Ultra Compact Stars

Compact object perturbations, at linear order, often lead in solving one or more coupled wave equations. The study of these equations was typically done by numerical or semi-analytical methods. The WKB method and the associated Bohr-Sommerfeld rule have been proved extremely useful tools in the study of black-hole perturbations and the estimation of the related quasi-normal modes. Here we present an extension of the aforementioned semi-analytic methods in the study of perturbations of ultra-compact stars and gravastars.

gr-qc↗