Seminar is held on Tuesdays at 13:10 pm in the lecture room of the Institute
on the 10th floor of the department building at Trója, V Holešovičkách 2, Prague 8
No seminars are planned for the near future.
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.
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.
The motion of a system of test point masses acting on one another in a curved spacetime is, in general, different from the motion of a single test point mass, i.e., different from a geodesic. The two effects which change the final trajectory of an extended body are called swinging and swimming. A simple example of such a body is a “glider” (or a "dumbbell") consisting of two point masses, whose coordinate distance can be modified as a function of time. We study the radial fall of this object described by a controlled Lagrangian along a radial in the Schwarzschild spacetime. We outline the published conclusions concerning this model and present our own results, which include the change of velocity of the dumbbell and the multiple-oscillations scenario. The deviation from the geodesic motion of the glider apparently diverges in the regions of very small and very large frequencies of oscillations. We offer a partial explanation of this behaviour in the low-frequency region and an estimate of the large critical frequencies. Further, we discuss the sufficiency of this model in these regions by studying the energy of the system and its compatibility with Dixon’s theory of extended bodies.
For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data. This gives rise to a conformal hyperboloidal initial data set for the vacuum conformal equations. When will the conformal data development of this initial data set be a conformal extension of a vacuum type D solution? In this work we provide an answer to this question. As an application of our construction we find a set of conditions for the data of the conformal equations which guarantees that its development is conformal to the Kerr solution.
Reciprocity relations in physics signal the existence of potentiality of a system. Maxwell-Betti reciprocity for virtual work in elasticity, Onsager’s reciprocity in thermodynamics or quantum mechanical reciprocity of the received signal all state that the observables are unchanged when the input and output agents are traversed. These distinct systems share a similar property: they are defined under some well-defined symplectic potential. The work we present here grew out of questioning what kind of potentiality Etherington’s distance reciprocity in relativity corresponds to. The outcome of such an investigation turns out to be a symplectic phase space reformulation of first order geometric optics within a Machian setting. This opens up a vast area of potential applications for astrophysical and cosmological light propagation scenarios which will also be summarized in this talk.
Jiří Bičák Oldřich Semerák