Department of Relativistic Astrophysics and Cosmology
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1. Sebastian J. Szybka, Syed U. Naqvi
Chaos and Einstein-Rosen waves
[abstract] [preprint] [arXiv]

We demonstrate the existence of chaotic geodesics for the Einstein-Rosen standing gravitational waves. The complex dynamics of massive test particles are governed by a chaotic heteroclinic network. We present the fractal associated with the system under investigation. Gravitational standing waves produce intricate patterns through test particles in a vague analogy to mechanical vibrations generating Chladni figures and complicated shapes of Faraday waves.

2. Krzysztof Głód, Szymon Sikora, Sebastian J. Szybka
Example of cross-polarized standing gravitational waves
Phys. Rev. D: Part. Fields , vol. 106, p. 124022 (2022).
[abstract] [preprint] [journal] [download]

We use a cosmological counterpart of the cylindrical Halilsoy solution to illustrate properties of cross-polarized standing gravitational waves.

3. Piotr T. Chru¶ciel, Sebastian J. Szybka
On the lag between deaths and infections in the first phase of the Covid-19 pandemic
[abstract] [preprint] [medRxiv]

One of the key issues in fighting the current pandemic, or the ones to come, is to obtain objective quantitative indicators of the effectiveness of the measures taken to contain the epidemic. The aim of this work is to point out that the lag between the daily number of infections and casualties provides one such indicator. For this we determined the lag during the first phase of the Covid-19 pandemic for a series of countries using the data available at the server of the John Hopkins University using three different methods. Somewhat surprisingly, we find a lag varying substantially between countries, taking negative values (thus the maximum daily number of casualties preceding the maximum daily number of new infections) in countries where no steps to contain the epidemic have been taken at the outset, with an average lag of $7\pm 0.3$ days. Our results can be useful to health authorities in a search for the best strategy to fight the epidemic.

4. Sebastian J. Szybka
Black Hole Flyby
Am. J. Phys., vol. 89, pp. 783-788 (2021).
[abstract] [preprint] [journal] [pdf]

We calculate the minimum distance at which one may approach a black hole in a free flyby. It corresponds to r=4m for the Schwarzschild black hole and a probe which was non-relativistic at infinity. The problem is formulated in a way that is useful for teaching introductory general relativity.

5. Sebastian J. Szybka, Syed U. Naqvi
Freely falling bodies in a standing-wave spacetime
Phys. Rev. D: Part. Fields , vol. 103, p. 024011 (2021).
[abstract] [preprint] [journal] [pdf]

We study the motion of free masses subject to the influence of standing gravitational waves in the polarized Gowdy cosmology with a three-torus topology. We show that antinodes attract freely falling particles and we trace the velocity memory effect.

6. Szymon Sikora, Krzysztof Głód
Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude
The European Physical Journal C, vol. 81, p. 208 (2021).
[abstract] [preprint] [journal]

We construct an approximate solution to the cosmological perturbation theory around Einstein–de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the metric, from which follows that the model density forms an infinite, cubic lattice. To verify the convergence of the perturbative construction, we express the resulting metric as a polynomial in the perturbative parameter and calculate the exact Einstein tensor. In our model, it seems that physical quantities averaged over large scales overlap with the respective Einstein–de Sitter prediction, while local observables could differ significantly from their background counterparts. As an example, we analyze the behavior of the local measurements of the Hubble constant and compare them with the Hubble constant of the homogeneous background model. A difference between these quantities is important in the context of a current Hubble tension problem.

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