13. Sebastian J. Szybka
On gravitational interactions between two bodies
In "Mathematical Structures of the Universe", eds. M. Eckstein, M. Heller, S. J. Szybka, CCPress, pp. 137-151 (2014).
[abstract] [preprint] [journal]

Abstract:
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only empirically determinable. We do not know if such a theory exists. Moreover, if it exists, there seems to be no reason for it to be comprehensible for the human mind. On the other hand, as pointed out in Wigner's famous paper, human mathematics is unbelievably successful in natural science. This seeming paradox may be mitigated by assuming that the mathematical structure of physical reality has many `layers'. As time goes by, physicists discover new theories that correspond to the physical reality on the deeper and deeper level. In this essay, I will take a narrow approach and discuss the mathematical structure behind a single physical phenomenon - gravitational interaction between two bodies. The main aim of this essay is to put some recent developments of this topic in a broader context. For the author it is an exercise - to investigate history of his scientific topic in depth.

14. Sebastian J. Szybka, Krzysztof Głód, Michał J. Wyrębowski, Alicja Konieczny
Inhomogeneity effect in Wainwright-Marshman space-times
Phys. Rev. D: Part. Fields , vol. 89, p. 044033 (2014).
[abstract] [preprint] [journal] [download]

Abstract:
Green and Wald have presented a mathematically rigorous framework to study, within general relativity, the effect of small scale inhomogeneities on the global structure of space-time. The framework relies on the existence of a one-parameter family of metrics that approaches the effective background metric in a certain way. Although it is not necessary to know this family in an exact form to predict properties of the backreaction effect, it would be instructive to find explicit examples. In this paper, we provide the first example of such a family of exact non-vacuum solutions to the Einstein's equations. It belongs to the Wainwright-Marshman class and satisfies all of the assumptions of the Green-Wald framework.

15. Mikko Lavinto, Syksy Rasanen, Sebastian J. Szybka
Average expansion rate and light propagation in a cosmological Tardis spacetime
JCAP, vol. 12, p. 051 (2013).
[abstract] [preprint] [journal] [download]

Abstract:
We construct the first exact statistically homogeneous and isotropic cosmological solution in which inhomogeneity has a significant effect on the expansion rate. The universe is modelled as a Swiss Cheese, with Einstein-de Sitter background and inhomogeneous holes. We show that if the holes are described by the quasispherical Szekeres solution, their average expansion rate is close to the background under certain rather general conditions. We specialise to spherically symmetric holes and violate one of these conditions. As a result, the average expansion rate at late times grows relative to the background, i.e. backreaction is significant. The holes fit smoothly into the background, but are larger on the inside than a corresponding background domain: we call them Tardis regions. We study light propagation, find the effective equations of state and consider the relation of the spatially averaged expansion rate to the redshift and the angular diameter distance.

16. Piotr T. Chruściel, Christa R. Ölz, Sebastian J. Szybka
Space-time diagrammatics
Phys. Rev. D: Part. Fields , vol. 86, p. 124041 (2012).
[abstract] [preprint] [journal] [download]

Abstract:
We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti) de Sitter family, with or without cosmological constant, and the Emparan-Reall black rings.

17. Piotr T. Chruściel, Michał Eckstein, Luc Nguyen and Sebastian J. Szybka
Existence of singularities in two-Kerr black holes
Class. Quantum Grav., vol. 28, p. 245017 (2011).
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Abstract:
We show that the angular momentum—area inequality 8π|J| ≤ A for weakly stable minimal surfaces would apply to I+-regular many-Kerr solutions, if any existed. Hence, we remove the undesirable hypothesis in the Hennig–Neugebauer proof of non-existence of well-behaved two-component solutions.
*supported by the grant from The John Templeton Foundation

18. Piotr T. Chruściel, Sebastian J. Szybka
Stable causality of the Pomeransky-Senkov black holes
Adv. Theor. Math. Phys., vol. 15, pp. 175-178 (2011).
[abstract] [preprint] [journal] [download]

Abstract:
We show stable causality of the Pomeransky-Senkov black rings.