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
When accretion onto a black hole occurs either at a fast or a slow rate, radiation stops cooling the accretion flow efficiently and the accretion disk becomes hot and geometrically thick. After a broader introduction to this topic, I will present new closed analytical solutions for geometrically thick fluid equilibria near black holes that can be used as initial conditions for simulations of such radiatively inefficient accretion flows. I will also show some simple magneto-hydrodynamic simulations in which we investigated possible consequences of varying the initial conditions for astrophysical predictions.
I will discuss conditions for the well-posedness of the initial value problem for evolution type PDEs. Well-posedness is a necessary condition for any numerical approximation to converge in the limit of infinite resolution. The crucial condition is that of strong-hyperbolicity. I will then consider various fluid models and highlight in particular the difficulties faced in particular in the modeling of stars. Several popular formulations of MHD turn out to be ill-posed.
I will present a generalisation of Derick theorem to the case of curved spacetime. As a consequence of this generalisation, relativistic boson stars are proved to be always unstable. Derrick’s theorem has profound consequences also on modified gravity, and in particular on theories with an additional scalar degrees of freedom. I will comment extensively on these consequences.
The search for the C-metric in higher dimensions is still unsuccessful and ongoing project. I wanted, also unsuccessfully, to find a simple solution to general boost-rotation symmetric metric in higher dimensions (generalization of Bonnor-Swaminayaran solutions). Finally I ended up in the linearized gravity to gain some insight in this topics and to learn some lessons. Based on work in progress this would be more discussion open seminar than a lecture.
The seminar will be devoted to investigation of possible solutions of the celebrated twistor equation on a special spacetime domain representing a black hole - an isolated horizon. First, the basic definitions and results on isolated horizons will be summarized. Than we move to definition of the so called Penrose mass and explain how it is connected to the twistor equation. Finally, we will discuss our results and future plans.
I will define classical and non-classical solutions of the wave equation. I will give some motivations about why low regularity scenarios are interesting. Finally, I will focus on the classical ones and discuss their relationship with quantum field theory in spacetimes with limited regularity.
Jiří Bičák Oldřich Semerák