Department of Relativistic Astrophysics and Cosmology
 
 
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1. 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.

2. 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.

3. Sebastian J. Szybka, Michał J. Wyrȩbowski
Backreaction for Einstein-Rosen waves coupled to a massless scalar field
Phys. Rev. D: Part. Fields , vol. 94, p. 024059 (2016).
[abstract] [preprint] [journal]

Abstract:
We present a one-parameter family of exact solutions to Einstein's equations that may be used to study the nature of the Green-Wald backreaction framework. Our explicit example is a family of Einstein-Rosen waves coupled to a massless scalar field.

4. A. Woszczyna, W. Czaja, K. Głód, Z. A. Golda, R. A. Kycia, A. Odrzywołek, P. Plaszczyk, L. M. Sokołowski, S. J. Szybka
ccgrg: The symbolic tensor analysis package with tools for general relativity
Wolfram Library Archive, vol. 8848 (2014).
[abstract] [journal]

Abstract:
Riemann and Weyl curvature, covariant derivative, Lie derivative, the first and the second fundamental form on hyper-surfaces, as well as basic notions of relativistic hydrodynamics (expansion, vorticity, shear) are predefined functions of the package. New tensors are easy to define. Instructions, basic examples, and some more advanced examples are attached to the package. Characteristic feature of the ccgrg package is the specific coupling between the functional programming and the Parker-Christensen index convention. This causes that no particular tools to rising/lowering tensor indices neither to the tensor contractions are needed. Tensor formulas are written in the form close to that of classical textbooks in GRG, with the only difference that the summation symbol appears explicitly. Tensors are functions, not matrixes, and their components are evaluated lazily. This means that only these components which are indispensable to realize the final task are computed. The memoization technique prevents repetitive evaluation of the same quantities. This saves both, time and memory.

5. 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.

6. 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.

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