Ústavu teoretické fyziky

Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK

v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8

V nejbližší budoucnosti nejsou plánované žádné semináře.

- 13. října 2015
- Separability of test fields / perturbations on the C-metric background
*David Kofroň*- ÚTF
- (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*- ÚTF
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*- ÚTF
- (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
- svátek
- 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*- ÚTF
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*- ÚTF
- 5. ledna 2016
- Seminář se nekoná
- 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.

- 1. března 2016
- Microlensing changes in quasar X-ray spectra
*Lukáš Ledvina*- ÚTF
- (seminář v angličtině)
- 8. března 2016
- GW150914: images rising from noise
*Tomáš Ledvinka*- ÚTF
- (seminář v angličtině)
- 15. března 2016
- Separability of test-field equations on the rotating C-metric background (including moral lesson)
*David Kofroň*- ÚTF
- (seminář v angličtině)
We present the separation of the Teukolsky master equation for the test field of arbitrary spin on the background of the rotating C-metric. We also summarize and simplify some known results about Debye potentials of these fields on type D background. The equation for the Debye potential is also separated.

Solving for the Debye potential of the electromagnetic field we show that on the extremely rotating C-metric no magnetic field can penetrate through the outer black hole horizon -- we thus recover the Meissner effect for the C-metric.

- 22. března 2016
- Near-infrared excess sources close to the supermassive black hole in the Galactic center
*Michal Zajaček*- Max Planck Institute for Radioastronomy, Bonn & First Institute of Physics, University of Cologne
- (seminář v angličtině)
- 28. března 2016
- Seminář se nekoná
- 5. dubna 2016
- Hairy times: Robinson-Trautman with a scalar field
*Tayebeh Tahamtan, Otakar Svítek*- ÚTF
- 12. dubna 2016
- Mimicking the dark sector with viscosity
*Giovanni Acquaviva*- ÚTF
- (seminář v angličtině)
- 19. dubna 2016
- Seminář se nekoná
*(od 14:00 přednáška A. Zakharova "The discovery of gravitational waves: past, present and future" na ÚTEF ČVUT na Albertově)*- 26. dubna 2016
- Optical matrix of type III in 6 dimensions or another stamp in the collection
*Jan Kubíček*- Matematický ústav AV ČR
- (seminář v angličtině)
The optical matrix of type III in 6D has been derived using Bianchi identities. It allows non-zero shear in an arbitrary dimension greater than four -- contrary to the famous Goldberg-Sachs theorem valid in 4D.

- 3. května 2016
- TBC or "The B=const": Constant magnetic field in GR
*Martin Žofka*- ÚTF
- (seminář v angličtině)
We derive a generalization of the Bonnor-Melvin solution where the cylindrically symmetric magnetic field is homogeneous. This requires a specific, non-vanishing cosmological constant. We investigate the properties of the spacetime and discover who discovered it.

- 10. května 2016
- Higher dimensional spacetimes with a separable Klein-Gordon equation
*Ivan Kolář*- ÚTF
- (seminář v angličtině)
We study a class of higher dimensional spacetimes that lead to a separable Klein-Gordon equation. Motivated by Carter's work in four dimensions, we introduce an ansatz for the separable metric in higher dimensions and find solutions of the Klein-Gordon equation. For such a metric we solve the Einstein equations and regain the Kerr–NUT–(A)dS spacetime and the Einstein-Kahler metric of a Euclidean signature. We construct a warped geometry of two Klein-Gordon separable spaces with a properly chosen warped factor. We show that the corresponding Klein-Gordon equation can also be solved by separation of variables. By solving the Einstein equations for the warped geometry we find new solutions.

- 17. května 2016
- Fluctuations and transport phenomena in horizon-fluids for black holes
*Swastik Bhattacharya, PhD*- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), Trivandrum, India
- (seminář v angličtině)
It is well-known that the black hole horizon obeys the equation of motion for a viscous fluid. A statistical model of this fluid can help us obtain some insight into the thorny problems of the microscopic black hole degrees of freedom and black hole entropy. In this talk, we shall take this fluid to be of a physical origin and construct a theory of fluctuations for it. In particular, I shall show that the Langevin equation governing the energy transported from outside into the horizon-fluid corresponds to the Raychaudhuri equation for the null congruences on the black hole horizon. We shall also briefly outline a method, that uses the Kubo formula to compute the coefficient of bulk viscosity of the horizon fluid. We shall show that this comes out to be negative due to the teleological nature of the black hole event horizon. Finally, I shall briefly outline how it is possible to have a statistical mechanical understanding of the negative specific heat of black holes in a similar manner.

- 24. května 2016
- Partial differential equations for sections of Hilbert bundles
*dr. Svatopluk Krýsl*- Matematický ústav, MFF UK
- (seminář v angličtině)
Partial differential equations are formulated and some of them quite well understood for single-valued (i.e. scalar) or vector-valued functions. The heat equation or the Laplace equation are examples of equations for scalar and the Maxwell equations are examples of those for vector fields. Their formulations on manifolds or on bundles over manifolds are known as well. PDEs for maps with values in specific Banach bundles were studied by Mishchenko and Fomenko (MSU) and their colleagues already in the seventies. They tried to generalize the Atiyah-Singer index theorem. In mathematics, their results became a part of so called analytic and geometric K-theory.

In Hodge theory one focuses on the systems of PDE's, more precisely, on the so called complexes of PDE's that are "elliptic". One of the important results of Hodge theory is the existence of an isomorphism of the cohomology of a complex with the kernel of generalized Laplacian associated uniquely to the complex. In the case of Banach bundles, the Hodge theory encounters crucial problems already at a topological level. The cohomology of such complexes may be an infinite dimensional TVS (which seems reasonable), but the induced topology on the cohomology does not separate points. Otherwise said, there exist convergent sequences whose limits can be any point of the vector space. Especially, it seems that no reasonable classical analysis on them is possible. In the current Physics, there is no known canonical way for choosing such a topology. There are no equations of physics which would determine it. Quite worrying is this situation in the case of the Becchi-Rouet-Stora-Tyutin (BRST) theory - a quantum field theory for constrained systems which gained a prominent role among theories on quantizing the gauges of potential type.

We explain basic notions briefly, give examples of the above-mentioned difficulties and show for which complexes one can get around them. Namely, the Hodge theory can be established for elliptic complexes on finitely generated projective K-bundles. One may imagine these bundles as bundles of state spaces whose fibers are acted upon by an algebra of observables in a way that they are finite with respect to this action. The projectivity means that the fibers are not too warped with respect to the observable algebra.

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*Jiří Bičák*
*Oldřich Semerák*

© 18. května 2016; Oldřich Semerák

© 26. května 2016; vygenerováno pomocí aplikace