Browsing Department of Physics by browse.metadata.advisor "Brink, Jeandrew"
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- ItemComputing the Arnold Tongue in the Zipoy-Voorhees Space-time(Stellenbosch : Stellenbosch University, 2017-03) Sherif, Abbas Mohamed; Brink, Jeandrew; Stellenbosch University. Faculty of Science. Dept. of PhysicsENGLISH ABSTRACT : In this thesis I study the integrability of the geodesic equations of the ZipoyVoorhees metric. The Zipoy-Voorhees spacetime is a one parameter family of Stationary Axisymmetric Vacuum spacetimes (SAV’s) that is an exact solution to the vacuum Einstein Field Equations (EFE’s). It has been conjectured that the end state of any asymptotically flat black hole formed by astrophysical mechanisms, such as for example, gravitational collapse of a star, merger of two black holes etc will be a characterised by the Kerr metric. The black hole will thus be a possibly rotating, stationary axisymmetric vacuum spacetime characterised by its mass and spin and will possess no closed time-like curves. Investigating orbits in the Zipoy-Voorhees spacetime serves as a concrete example to of how the Kerr hypothesis fails. For this metric, I compute the Poincaré map and then compute the rotation curve. The Poincaré map is a tool to locate the region where chaos occurs in a dynamical system. The rotation curve is used to quantify chaos in the system. I focus my study on the 2/3 resonance for a range of the parameter values δ ∈ [1, 2]. The value δ = 1 corresponds to the Schwarzschild solution where the system is integrable. I then compute the Arnold tongue by plotting the size of the resonant regions against the parameter values to quantify the departure from integrability. I find that the shape of the tongue of instability is nonlinear and the Arnold tongue pinches off at δ = 1.6.
- ItemGeodesics and resonances of the Manko-Novikov spacetime(Stellenbosch : Stellenbosch University, 2013-03) Geyer, Marisa; Brink, Jeandrew; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: In this thesis I study compact objects described by the Manko-Novikov spacetime. The Manko- Novikov spacetime is an exact solution to the Einstein Field Equations that allows objects to be black hole-like, but with a multipole structure di erent from Kerr black holes. The aim of the research is to investigate whether we will observationally be able to tell these bumpy black holes, if they exist, apart from traditional Kerr black holes. I explore the geodesic motion of a test probe in the Manko-Novikov spacetime. I quantify the motion using Poincar e maps and rotation curves. The Manko-Novikov spacetime admits regions with regular motion as well as regions with chaotic motion. The occurrence of chaos is correlated with orbits for which the characteristic frequencies are resonant. The new result presented in this thesis is a global characterisation of where resonances and thus chaos are likely to occur for all orbits. These calculations are performed in the Kerr spacetime, from which I obtain that low order resonances occur within 20 Schwarzschild radii (or 40M) of the compact object with mass M. By the KAM theorem, the occurrence of chaos is therefore limited to this region for all small perturbations from Kerr. These resonant events will be measurable in the Galactic Centre using eLISA. This con nement of low order resonances indicates that the frequency values of orbits of radii well outside of 20 Schwarzschild radii can be approximated using canonical perturbation theory.