Relativistický seminář
Ústavu teoretické fyziky

podzim 2015

Proběhlé semináře:

13. října 2015
Separability of test fields / perturbations on the C-metric background
David Kofroň
(seminář v angličtině)

If NP formalism is applied to the D-type spacetimes, the equations for outermost (ingoing and outgoing radiation) components of (a) mass-less Klein-Gordon field (s=0), (b) neutrino field (s=1/2), (c) test Maxwell field (s=1), (d) Rarita-Schwinger field (s=3/2) and gravitational perturbations are decoupled. I write all of them in GHP formalism, and then obtain equation analogous to Teukolsky master equation (originally for Kerr-Newman metric) for charged C-metric. I show that solution of these equation can be found using separation of variables in the canonical coordinates. The angular part of the solution leads to generalized "accelerated spin weighted spherical harmonics". These are in general Heun functions, but for extremal case the solutions reduce to rational functions. I find the eigenfunctions and eigenvalues for axially symmetric fields (m=0) and show why for m different from zero this is complicated, solving the same problem for cosmic string spacetime (the C-metric inherently contains deficit angle).

20. října 2015
Quasilocal horizons
Eliška Klozová

Since the event horizon has some drawbacks because of its global definition, a quasilocal horizon has been introduced. It is a hypersurface foliated by marginally trapped surfaces on which expansion of the outer null normal congruence vanishes. Different types of quasilocal horizons will be listed, i.e. apparent horizon, trapping horizon and isolated and dynamical horizons. Analysis of quasilocal horizons in two dynamical spacetimes used as inhomogeneous cosmological models will also be presented. We discovered future and past horizon in spherically symmetric Lemaître spacetime. Both horizons are null and have locally the same geometry as the horizons in the LTB spacetime. Then we studied Szekeres-Szafron spacetime with no symmetries, particularly its subfamily with non-zero beta,z, and we derived the equation of the horizon. However, because of the lack of symmetries the space-time is not adapted to double-null foliation, therefore our attempts to estimate the equation´s solution were unsuccessful.

27. října 2015
Cosmology beyond the linear and Newtonian approximations
dr. Eleonora Villa
Institute of Cosmology and Gravitation, University of Portsmouth, UK
(seminář v angličtině)

Roughly speaking, cosmologists study large, linear scales and small, non-linear scales in two different ways: relativistic perturbation theory around a homogeneous and isotropic background describes scales where the growth of structures is at an early stage. At smaller scales, well inside the Hubble horizon, the relativistic effects are supposed to be completely negligible and General Relativity is replaced by Newtonian gravity. A post-Newtonian type approximation is a crucial improvement of this simple paradigm as it bridges the gap between relativistic perturbation theory and Newtonian structure formation. I focus on the relativistic corrections corrections for both the Eulerian and the Lagrangian approaches to gravitational dynamics in standard perturbation theory and in the post-Newtonian approximation. I finally present the post-Newtonian extension of the Zel'dovich solution for the plane parallel dynamics and its application in the context of the cosmological back-reaction proposal.

3. listopadu 2015
Thermodynamics of the gravitational field
dr. Giovanni Acquaviva
Department of Mathematical Sciences, University of Zululand, Kwa-Dlangezwa, South Africa
(seminář v angličtině)

In the task of describing the history of our Universe - considered as a solution of the field equations of General Relativity - we analyse the issue of including the spacetime geometry as a thermodynamic actor along with the matter degrees of freedom. We show how it is possible to associate thermodynamic features to the free gravitational field in a purely geometrical way, following a proposal conceptualized by Penrose and recently formalized by different authors. We apply the resulting framework in the context of structure formation under the effect of gravity: the chain of processes leading from small matter inhomogeneities to black holes is shown to satisfy a "second law" of non-decreasing entropy. An interesting link to the thermodynamics of horizons is also presented. Eventually we contemplate the possibility of using the second law as a guiding principle for selecting thermodynamically favourable gravitational configurations: in this regard, an application to the Cosmic Censorship of naked singularities is briefly discussed.

10. listopadu 2015
Disks as sources of the Tomimatsu-Sato spacetimes
Tomáš Ledvinka
(seminář v angličtině)

We describe the properties of disk sources of the gravitational field matching the first three members of the Tomimatsu-Sato family of stationary axisymmetric, asymptotically flat vacuum spacetimes (among them is the well-known Kerr solution). We cut out the central region containing singularities and by a proper identification we get a disk-like distribution of stress-energy tensor. If the cut-out region is large enough, realistic models of disk material can be found, e.g. in the form of counter-rotating streams of particles. We discuss how energy conditions become violated and possibility to find realistic models of disk material is lost once the cut-out region becomes small enough and how it relates to the cosmic censorship conjecture. We show that this prevents the construction of 'realistic' disks surrounded by regions of closed time-like curves which appear in the the Tomimatsu-Sato spacetimes.

17. listopadu 2015
24. listopadu 2015
Spacetimes of Weyl and Ricci type N in higher dimensions
Martin Kuchynka
Matematický ústav, MFF UK

We study geometrical properties of null congruences generated by an aligned null direction of the Weyl tensor (WAND) in spacetimes of the Weyl and Ricci type N in an arbitrary dimension. We prove that non-aligned Ricci type N spacetimes of the genuine Weyl type III or N do not exist and for aligned Weyl type III and N, Ricci type N spacetimes, the multiple WAND is geodetic. For aligned Weyl and Ricci type N spacetimes, the canonical form of the optical matrix in the twisting and non-twisting case is derived and the dependence of the Weyl tensor and the Ricci tensor on an affine parameter of the geodetic null congruences generated by the WAND is obtained. Finally, examples of higher-dimensional Weyl and Ricci type N spacetimes with various possible geometries of their multiple WANDs are constructed as direct products of four-dimensional pure radiational metrics with the Euclidean space.

1. prosince 2015
Gamma Ray Bursts. The death throes of massive stars
Prof. Agnieszka Janiuk
Center for Theoretical Physics, Polish Academy of Sciences, Warsaw
(seminář v angličtině)

Gamma Ray Bursts are short, transient events, observed isotropically on the sky at a rate of up to a few times per day. The energetics of the bursts indicates that they must be associated with a cosmic explosion of enormous power, when a new black hole is born and accretes material from its surrounding at a very high rate. This process leads to the formation of ultra-relativistic jets moving with Lorentz factors up to ~ 200-1000. Observations show that long GRBs are associated with the collapse of massive stars, often accompanied by energetic supernovae. As the jet breaks out of the star and freely expands in the environment, dissipation of kinetic energy in internal shocks and/or at the jet photosphere produces the gamma-ray emission (the "prompt emission"). When the jet decelerates, it produces a multi-wavelength afterglow which can be observed in radio over several years. Hidden from direct observation is the "central engine" which is sustaining the production of the relativistic jet.

In this talk, a particular focus will be given to describe the GRB central engine that is powered by the collapse of a massive rotating star. The engine is a hot and dense accretion disk, formed around a rotating black hole and composed of a very dense matter, where free nucleons, electron-positron pairs and helium are present, and cooling is due to neutrino emission. A significant number density of neutrons in the disk provides conditions for a neutron-rich plasma in the GRB outflows or jets. Also, heavy nuclei are formed in the outer disk as well as in the outflowing material. I will discuss the MHD and HD models of the GRB engine and the results of nuclear-reaction network computations. I will also describe a speculative scenario for the longest-duration GRBs, resulting from the collapse of a massive rotating star in a close binary system with a companion black hole. After the infall and spiral-in toward the primary, the two BHs merge inside the circumbinary disk. The second episode of mass accretion and high final spin of the post-merger BH prolongs the GRB central-engine activity. The observed events should have two distinct peaks in the electromagnetic signal, separated by a gravitational wave emission. The gravitational recoil of the burst engine is also possible.
1. prosince 2015
!!! Mimořádně v 15:30 !!!
Many faces of constraints
Prof. István Rácz
Wigner Research Center for Physics, Budapest
(seminář v angličtině)
8. prosince 2015
Meissner effect for astrophysically relevant black holes
Martin Scholtz

Extremal black holes tend to expel magnetic field lines from the horizon. Since the temperature of extremal black hole vanishes, this effect is analogous to the well-known Meissner effect for superconductors. The presence of the black hole Meissner effect has been demonstrated in many particular situations, especially (but not only) in the cases when the electromagnetic field is treated as a test field. In this talk, we present an exact result that EM field is expelled from the horizon of arbitrary stationary, axially symmetric black hole, provided that the field shares the symmetries of the spacetime.

15. prosince 2015
Summary of the anniversary Berlin conference "A Century of GR"
Jiří Podolský, Pavel Krtouš
12. ledna 2016
Asymptotická bezpečnost jako cesta ke kvantové teorii gravitace
dr. Martin Zdráhal
Ústav částicové a jaderné fyziky, MFF UK

Nalezení kvantové teorie gravitace se stalo jednou z největších výzev teoretické fyziky. Zatímco většina fyziků zabývajících se touto výzvou po prvotních neúspěších opustila cestu kvantové teorie pole (QFT) a vrhla se na různé alternativy (teorie strun, smyčková gravitace, kauzální dynamická triangulace, ...), v poslední době se ukazuje, že s využitím předpokladu o asymptotické bezpečnosti by bylo možné překonat potíže s kvantováním gravitace v rámci QFT. V průběhu tohoto semináře se pokusím jednoduchým způsobem vysvětlit základní předpoklady, na kterých je tento přístup postaven, a ukážu několik zajímavých výsledků, ke kterým došel.

Další ročníky:

© 5. října 2016; Oldřich Semerák <>
© 6. října 2016; vygenerováno pomocí aplikace seminar, verze 2.04 (2003-09-02); správce <>