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1. Sebastian J. Szybka, Adam Cieślik On standing waves in general relativity , vol. xxx, pp. xxxxxx (2019). [abstract] [preprint]  Abstract: We propose a covariant definition of standing gravitational waves in general relativity.  2. Sebastian J. Szybka, Mieszko Rutkowski Einstein clusters as models of inhomogeneous spacetimes Journal, vol. xxx, pp. xxxxxx (2019). [abstract] [preprint] [journal]  Abstract: We study the effect of smallscale inhomogeneities for Einstein clusters. We construct a spherically symmetric stationary spacetime with smallscale 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 toymodel for studies of the effect of smallscale inhomogeneities in general relativity.  3. Piotr T. Chruściel, Sebastian J. Szybka, Paul Tod Towards a classification of vacuum nearhorizons geometries Class. Quantum Grav. 35 (2018) 015002, vol. 35, p. 015002 (2018). [abstract] [preprint] [journal]  Abstract: We prove uniqueness of the nearhorizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum nearhorizon geometries.  4. Sebastian J. Szybka, Michał J. Wyrȩbowski Backreaction for EinsteinRosen waves coupled to a massless scalar field Phys. Rev. D: Part. Fields , vol. 94, p. 024059 (2016). [abstract] [preprint] [journal]  Abstract: We present a oneparameter family of exact solutions to Einstein's equations that may be used to study the nature of the GreenWald backreaction framework. Our explicit example is a family of EinsteinRosen waves coupled to a massless scalar field.  5. 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 hypersurfaces, 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 ParkerChristensen 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.  6. 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. 137151 (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.  
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