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The Numerical Evolution of Neutron Star Oscillations

Johannes Ruoff
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Abstract

The present work investigates the numerical evolution of linearized oscillations of non-rotating, spherically symmetric neutron stars within the framework of general relativity. We derive the appropriate equations using the (3+1)-formalism. We first focus on the evolution of radial oscillations, which do not emit gravitational waves. We demonstrate how to handle a numerical instability that also occurs in the non-radial case, when the stellar model is constructed based on a realistic equation of state. We devise a coordinate transformation that not only removes this instability but also provides much more accurate results. [...] The main part deals with the evolution of non-radial oscillations (l >= 2) of neutron stars. Here, we compare different formulations of the equations and discuss how they have to be numerically dealt with in order to avoid instabilities at the origin. We present results for various polytropic stellar models and different initial data. [...] In the last part of this thesis we consider a physical mechanism for exciting oscillations of neutron stars. We use the time dependent gravitational field of a small point mass μthat orbits the neutron star to induce stellar oscillations. With this particle we have a physical means which removes the arbitrariness in choosing the initial data. [...] By sampling various orbital parameters of the particle we show that in general the particle is not able to excite any w-modes. It is only for speeds very close to the speed of light that the w-mode is a significant part of the wave signal.

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Johannes Ruoff. 2000-10-10. The Numerical Evolution of Neutron Star Oscillations. https://arxiv.org/abs/gr-qc/0010041

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