RESEARCH GROUP

MATHEMATICAL STRUCTURES OF THE UNIVERSE

Selected publications

 
   
   
   
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1. Krzysztof Głód
1+1+2 covariant formulation of light propagation in spacetime
Phys. Rev. D: Part. Fields , vol. 101, p. 024021 (2020).
[abstract] [journal]

Abstract:
We present a covariant approach to the problem of light beam propagation in a spacetime. We develop our considerations within the framework of classical geometric optics in general relativity. Using the concept of a screen surface orthogonal to the observer velocity and to the bundle of geodesics, we introduce covariant four-dimensional definitions for Sachs and Jacobi optical fields and for the area distance. Then we give relationships between them and derive their propagation equations together with initial conditions for these equations. Ultimately, for practical use, we transform the resulting formulas into the redshiftdependent form.

2. Piotr T. Chruściel, Sebastian J. Szybka
A phenomenological algorithm for short-range predictions of the Covid-19 pandemic 2020
(2020).
[abstract] [preprint] [medrxiv]

Abstract:
We present an algorithm for dynamical fitting of a logistic curve to the Covid-19 epidemics data, with fit-parameters linearly evolving to the future. We show that the algorithm would have given reasonable short- and medium-range predictions for the mid-range evolution of the epidemics for several countries. We introduce the double-logistic curve, which provides a very good description of the epidemics data at any given time of the epidemics. We analyse the predictability properties of some naive models.

3. Piotr T. Chruściel, Sebastian J. Szybka
Universal properties of the dynamics of the Covid-19 pandemics
(2020).
[abstract] [preprint] [journal] [pdf]

Abstract:
We present evidence for existence of a universal lower bound for the initial growth rate of the epidemic curve of the SARS-CoV-2 coronavirus. This can be used to infer that, on average, an asymptomatic infected individual is infectious during 5.6 plus/minus 0.3 days. We further present evidence of an average time scale of 12 days for halving the number of new cases, or new deaths, during the extinction period of the first phase of the epidemic.

4. Sebastian J. Szybka
Some remarks on the first image of a black hole
Philosophical Problems in Science, vol. 68, pp. 281-294 (2020).
[abstract] [journal] [pdf]

Abstract:
On the 10th of April, 2019 the Event Horizon Telescope Collaboration presented the first image of the black hole. The image was obtained with a planet-scale array of eight ground-based radio telescopes. The observation relied on a technique called very long base interferometry which synchronises telescope facilities around the world. The image of a black hole together with the recent detections of gravitational waves confirms one of the most intriguing predictions of Einstein’s gravity theory, namely, the existence of black holes. I will provide more details on this remarkable observation and explore its consequences for our understanding of nature. The physical reality of black holes is strongly supported by recent advances of astronomy. I claim that this fact is the key to understanding the relation between our world and the world of mathematics.

5. Sebastian J. Szybka, Mieszko Rutkowski
Einstein clusters as models of inhomogeneous spacetimes
Eur. Phys. J. C, vol. 80, p. 397 (2020).
[abstract] [preprint] [journal] [springer]

Abstract:
We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric static spacetime with small-scale radial inhomogeneities and propose the Gedankenexperiment. An hypothetical observer at the center constructs, using limited observational knowledge, a simplified homogeneous model of the configuration. An idealization introduces side effects. The inhomogeneous spacetime and the effective homogeneous spacetime are given by simple solutions to Einstein equations. They provide a basic toy-model for studies of the effect of small-scale inhomogeneities in general relativity. We show that within our highly inhomogeneous model the effect of small-scale inhomogeneities remains small for a central observer. The homogeneous model fits very well to all hypothetical observations as long as their precision is not high enough to reveal a tension.

6. Sebastian J. Szybka, Adam Cieślik
Standing waves in general relativity
Phys. Rev. D: Part. Fields , vol. 100, p. 064025 (2019).
[abstract] [preprint] [download]

Abstract:
We propose a covariant definition of standing gravitational waves in general relativity.

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