1. Sebastian J. Szybka, Adam A. Zychowicz, Dominika Hunik
Backreaction of Halilsoy and Chandrasekhar waves
Phys. Rev. D: Part. Fields , vol. 113, p. 084006 (2026).
[abstract] [preprint] [journal]

Abstract:
We calculate the high-frequency limit of the Halilsoy and Chandrasekhar standing gravitational wave solutions. We show that the backreaction effect is the same for these classes of solutions and we analyze the causal structure of the effective spacetime. In addition, we rederive both classes of solutions without referring to the Ernst equation and generation techniques.

2. Kornelia Nikiel, Sebastian J. Szybka
Halilsoy and Chandrasekhar standing gravitational waves in the linear approximation
Phys. Rev. D: Part. Fields , vol. 111, p. 104015 (2025).
[abstract] [preprint] [journal] [download]

Abstract:
Halilsoy and Chandrasekhar cylindrical standing gravitational waves correspond to two different classes of solutions to the vacuum Einstein equations. Both families satisfy the definition of standing gravitational waves proposed by Stephani, but only the latter class fulfills the stricter definition introduced by Chandrasekhar. The aim of this research is to compare both classes of solutions within the linear regime. We discover that the linearized Halilsoy and Chandrasekhar standing waves are gravitational analogues of two different types of electromagnetic polarization standing waves.

3. Sebastian J. Szybka, Syed U. Naqvi
Chaos and Einstein-Rosen gravitational waves
Phys. Rev. D: Part. Fields , vol. 108, p. L081501 (2023).
[abstract] [preprint] [journal] [arXiv]

Abstract:
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.

4. 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]

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

5. Piotr T. Chruściel, Sebastian J. Szybka
On the lag between deaths and infections in the first phase of the Covid-19 pandemic
(2021).
[abstract] [preprint] [medRxiv]

Abstract:
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.

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

Abstract:
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.