Already in his bachelor thesis, V. Witzany wrote a symplectic integrator and employed it for a study of free motion in a pseudo-Newtonian field mimicking the gravitational system of a black hole surrounded by a thin disc or ring. He should now finish this study, comparing the results obtained for several different simple potentials with those yielded by an exact general relativistic system. The comparison should be performed on Poincaré diagrams endowed with information provided by some of the Lyapunov-type coefficients (probably the MEGNO) or recurrence-analysis quantifiers (probably the DIV indicator). It would also be desirable to check the results by the code recently developed by Seyrich & Lukes-Gerakopoulos. Finally, a more advanced future programme would be to extend the analysis to a stationary case (involving rotation), using the metrics found by linear-perturbation techniques.
Seznam odborné literatury
Lowenstein J. H.: Essentials of Hamiltonian Dynamics (Cambridge Univ. Press, Cambridge 2012)
Broer H., Takens F.: Dynamical Systems and Chaos (Springer, Berlin Heidelberg 2011)
Hirsch M. W., Smale S., Devaney R. L.: Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd ed. (Academic Press, Elsevier 2013)
články z odborných časopisů
Předběžná náplň práce
Black holes supposed to drive astrophysical sources are usually being modelled by the Kerr metric, but in reality they are neither isolated nor stationary, and they also do not seem to live in an asymptotically flat space-time. This queries the relevance of various black-hole theorems, but also, for example, spoils the complete integrability of geodesic equation. We have studied the geodesic dynamics in simple, static and axially symmetric exact space-times generated by an (originally) Schwarzschild black hole surrounded by an annular thin disc or ring, and observed how the motion of free test particles becomes chaotic for sufficiently large mass of the additional source and sufficiently large particle energy. The study can now be continued in different ways, for example, by checking our previous results using a different type of integrator, by comparing them with those obtained in a “corresponding” (pseudo-)Newtonian systems, by employing different methods and chaos indicators, or, in particular, by extending it to a stationary setting when the sources are allowed to rotate (this might be achieved using a metric obtained within a linear-perturbation approximation).
Předběžná náplň práce v anglickém jazyce
Black holes supposed to drive astrophysical sources are usually being modelled by the Kerr metric, but in reality they are neither isolated nor stationary, and they also do not seem to live in an asymptotically flat space-time. This queries the relevance of various black-hole theorems, but also, for example, spoils the complete integrability of geodesic equation. We have studied the geodesic dynamics in simple, static and axially symmetric exact space-times generated by an (originally) Schwarzschild black hole surrounded by an annular thin disc or ring, and observed how the motion of free test particles becomes chaotic for sufficiently large mass of the additional source and sufficiently large particle energy. The study can now be continued in different ways, for example, by checking our previous results using a different type of integrator, by comparing them with those obtained in a “corresponding” (pseudo-)Newtonian systems, by employing different methods and chaos indicators, or, in particular, by extending it to a stationary setting when the sources are allowed to rotate (this might be achieved using a metric obtained within a linear-perturbation approximation).
- zadáno a potvrzeno stud. odd.