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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]

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

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

3. Sebastian J. Szybka, Mieszko Rutkowski
Einstein clusters as models of inhomogeneous spacetimes
Journal, vol. xxx, pp. xxx-xxx (2019).
[abstract] [preprint] [journal]

We study the effect of small-scale inhomogeneities for Einstein clusters. We construct a spherically symmetric stationary 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 tensions and side effects. The inhomogeneous spacetime and the effective homogeneous spacetime are given by exact solutions to Einstein equations. They provide a simple toy-model for studies of the effect of small-scale inhomogeneities in general relativity.

4. 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]

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.

5. 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]

We prove uniqueness of the near-horizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum near-horizon geometries.

6. Szymon Sikora, Krzysztof Głód
Example of an inhomogeneous cosmological model in the context of backreaction
Phys. Rev. D: Part. Fields , vol. 95, p. 063517 (2017).
[abstract] [preprint] [journal]

In this article, we present an example of an inhomogeneous cosmological model, which is inspired by the linear perturbation theory. The metric of this model can be described as the Einstein–de Sitter background with periodically distributed dust overdensities. The model construction enables application of the Green-Wald averaging scheme and the Buchert averaging technique simultaneously. We compare the angular diameter distance function of the considered model to the angular diameter distances corresponding to the average space-times given by the Green-Wald and the Buchert frameworks respectively.

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