Department of Relativistic Astrophysics and Cosmology
 
 
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19. Christa R. Ölz, Sebastian J. Szybka
Conformal and projection diagrams in LaTeX
(2013).
[abstract] [preprint]

Abstract:
In general relativity, the causal structure of space-time may sometimes be depicted by conformal Carter-Penrose diagrams or a recent extension of these - the projection diagrams. The introduction of conformal diagrams in the sixties was one of the progenitors of the golden age of relativity. They are the key ingredient of many scientific papers. Unfortunately, drawing them in the form suitable for LaTeX documents is time-consuming and not easy. We present below a library that allows one to draw an arbitrary conformal diagram in a few simple steps.

20. Leszek M. Soko³owski
On the twin paradox in static spacetimes: I. Schwarzschild metric
General Relativity and Gravitation, vol. 44, pp. 1267-1283 (2012).
[abstract] [preprint]

Abstract:
Abstract Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics.We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry. Keywords twin paradox · static spacetimes · Jacobi fields · conjugate points *supported by the grant from The John Templeton Foundation

21. Piotr T. Chru¶ciel, 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.

22. Sikora S, Bratek £., Ja³ocha J., Kutschera M.
Gravitational microlensing as a test of a finite-width disk model of the Galaxy
Astron. Astrophys. , vol. 546, p. A126 (2012).
[abstract] [preprint] [journal] [download]

Abstract:
The aim of this work is to show, in the framework of a simple finite-width disk model, that the amount of mass seen through gravitational microlensing measurements in the region 0 < R < R◦ is consistent with the dynamical mass ascertained from Galaxy rotation after subtracting gas contribution. Since microlensing only detects compact objects, this result suggests that a non-baryonic mass component may be negligible in this region.

23. Piotr T. Chru¶ciel, Micha³ Eckstein, Luc Nguyen and Sebastian J. Szybka
Existence of singularities in two-Kerr black holes
Class. Quantum Grav., vol. 28, p. 245017 (2011).
[abstract] [preprint] [journal]

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

24. Piotr T. Chru¶ciel, 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.

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