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
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie Series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces well-known relativistic effects such as the precession of the pericentre and the Lense-Thirring and geodetic effects. Additionally, our theory takes into full account the complex interplay between the various relativistic effects, and provides a new explicit solution of the averaged equations of motion in terms of elliptic functions. Our analysis reveals the presence of particular configurations for which non-periodical behaviour can arise. The application of our results to real astrodynamical systems (such as Mercury-like and pulsar planets) highlights the contribution of relativistic effects to the long-term evolution of the spin and orbit of the secondary body.
I will introduce two different inhomogeneous cosmological models one of which is based on a regular lattice of black holes and a second one following the Geroch-Stephani generating technique. The second part will explain how dark energy and the inflation field can be modeled through the non-ideal equation of state of Shan-Chen accounting for their microscopical foundations and the motion of test particles undergoing scattering effect according to the Poynting-Robertson model and I will conclude mentioning a local way of detecting the horizon of a black hole in terms of the zeros of Cartan invariants.
Corvino (2000) showed that any given asymptotically flat and conformally flat initial data set can be truncated and glued along an annulus to a Schwarzschild metric in the exterior. It will be shown that this powerful result can be implemented numerically in an axisymmetric setting: a Schwarzschildean end will be glued to Brill-Lindquist data describing two non-rotating black holes. The total ADM mass of the resulting space-time will be computed and its dependence on the details of the gluing construction will be thorough investigated.
For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.
It has been suggested that relativistic shocks in extragalactic sources may accelerate the highest energy cosmic rays, but recent theoretical advances indicate that relativistic shocks are probably unable to accelerate particles to energies much larger than a PeV. We study the hotspots of radiogalaxies. The observed turnover of the synchrotron spectrum indicates that the maximum energy of electrons accelerated at the jet termination shock is less than 1 TeV in a 100 microG magnetic field. We show that this maximum energy cannot be constrained by synchrotron losses as usually assumed. We propose that the maximum energy is determined by ceasing the cross-field diffusion in a perpendicular 1 microG magnetic field. We demonstrate that Bell instabilities generated by the streaming of cosmic rays with the same energy as the most energetic electrons in the hotspot can amplify the turbulent field up to 100 microG. If the maximum energy of electrons is determined by the diffusion condition, the same limit applies to protons and therefore the maximum energy of ions is also less than 1 TeV. As a consequence, relativistic jet termination shocks are poor cosmic ray accelerators. We test this result by considering the radiogalaxy Cygnus A as a case study.
Jiří Bičák Oldřich Semerák