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. 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. |
4. 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. |
5. Szymon Sikora, Krzysztof Głód Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities Phys. Rev. D: Part. Fields , vol. 99, p. 083512 (2019). [abstract] [preprint] [journal] |
Abstract: We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter λ, we are able to achieve large values of the density contrast. With a metric explicitly given, many model properties can be calculated in a straightforward way which is interesting in the context of the current discussion concerning the averaging of the inhomogeneities and their backreaction in cosmology. Although the Einstein-de Sitter model can be thought of as the model average, the light propagation differs from that of Einstein-de Sitter. The angular diameter distance-redshift relation is affected by the presence of inhomogeneities and depends on the observer’s position. The model construction scheme enables some generalizations in the future, so the present work is a step toward more realistic cosmological model described by a relatively simple analytical metric. |
6. Piotr T. Chruściel, Sebastian J. Szybka, Paul Tod Towards a classification of vacuum near-horizons geometries Class. Quantum Grav. 35 (2018) 015002, vol. 35, p. 015002 (2018). [abstract] [preprint] [journal] |
Abstract: We prove uniqueness of the near-horizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum near-horizon geometries. |