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25. 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.  26. Bratek Ł., Sikora S., Jałocha J., Kutschera M. A lower bound on the Milky Way mass from general phasespace distribution function models Astron. Astrophys. , vol. 562, p. A134 (2014). [abstract] [preprint] [journal] [download]  Abstract: We model the phasespace distribution of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within ≈150−200 kpc. By approximating the potential as Keplerian, the phasespace distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We systematically construct a family of phasespace functions with the resulting radial velocity dispersion overlapping with the one obtained using data on radial motions of distant kinematic tracers, while making no assumptions about the density of the tracers and
the velocity anisotropy parameter β regarded as a function of the radial variable. While there is no apparent upper bound for the Milky Way mass, at least as long as only the radial motions are concerned, we find a sharp lower bound for the mass that is small. In particular, a mass value of 2.4e11 solar mass, obtained in the past for lower and intermediate radii, is still consistent with the dispersion profile at larger radii. Compared with much greater mass values in the literature, this result shows that determining the Milky Way mass is strongly modeldependent. We expect a similar reduction of mass estimates in models assuming more realistic mass profiles.
 27. Jałocha J., Sikora S., Bratek. Ł, Kutschera M. Constraining the vertical structure of the Milky Way rotation by microlensing in a finitewidth global disk model Astron. Astrophys. , vol. 566, p. A87 (2014). [abstract] [preprint] [journal]  Abstract: We model the vertical structure of mass distribution of the Milky Way galaxy in the framework of a finitewidth global disk model. Assuming only the Galactic rotation curve, we tested the predictions of the model inside the solar orbit for two measurable processes that are unrelated to each other: the gravitational microlensing that allows one to fix the disk widthscale by the best fit to measurements, and the vertical gradient of rotation modeled in the quasicircular orbits approximation. The former is sensitive to the gravitating mass in compact objects, the latter to all kinds of gravitating matter. The analysis points to a small widthscale of the considered disks and an atmost insignificant contribution of nonbaryonic dark matter in the solar circle. The predicted high vertical gradient values in the rotation are consistent with the gradient measurements.  28. 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.  29. Sebastian J. Szybka, Krzysztof Głód, Michał J. Wyrębowski, Alicja Konieczny Inhomogeneity effect in WainwrightMarshman spacetimes 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 spacetime. The framework relies on the existence of a oneparameter 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 nonvacuum solutions to the Einstein's equations. It belongs to the WainwrightMarshman class and satisfies all of the assumptions of the GreenWald framework.  30. Editors: Michał Eckstein, Michael Heller, Sebastian J. Szybka Mathematical Structures of the Universe Copernicus Center Press (2014) [abstract] [journal]  Abstract: The book contains a collection of essays on mathematical structures that serve us to model the Universe. The authors discuss such topics as: the interplay between mathematics and physics, geometrical structures in physical models, observational and conceptual aspects of cosmology. The reader can also contemplate the scientific method on the verge of its limits.  
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