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
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.
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.
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.
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).
Jiří Bičák Oldřich Semerák