Statistics – Computation
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phdt........24d&link_type=abstract
PhD Thesis, Proquest Dissertations And Theses 2005. Section 0090, Part 0606 214 pages; [Ph.D. dissertation].United States -- Ill
Statistics
Computation
Compact Stars, General Relativity, Relativistic Astrophysics, Computational Astrophysics
Scientific paper
Due to the strong spacetime curvature in the vicinity of neutron stars and black holes, the structure and dynamics of these objects and of systems containing them can only understood using full general relativity without approximations. The Einstein field equations which determine the spacetime metric can only be solved analytically in very special cases. In the more general cases of interest, the Einstein equations must be solved numerically. We have developed a code to simulate the evolution of spacetimes in the presence of various forms of matter. This is done by integrating the Einstein field equations coupled to the equations of motion for the matter. In particular, we have studied the evolution of systems containing hydrodynamic or magnetohydrodynamic matter. Our code can be applied to many systems of astro-physical interest. Here we have focused on issues relating to the evolution of rapidly rotating neutron stars.
Our spacetime evolution scheme is based on the BSSN formulation of the Einstein equations, but we introduce several modifications to the BSSN equations to improve stability. Also, we introduce new dynamical gauge conditions which produce desirable features in the behavior of the coordinate system. Black hole spacetimes are treated using singularity excision. We develop the first excision code capable of performing long-time evolutions of black hole spacetimes with matter. Our code is also the first fully relativistic code to simulate viscous fluids (by evolving the coupled Einstein-Navier-Stokes equations) and magnetized fluids (by evolving the coupled Einstein-Maxwell-MHD equations) in dynamical spacetimes.
We study the effect of rotation on the gravitational collapse of a compact star to a black hole. We find that centrifugal forces halt the collapse if the rotation is supra-Kerr ( J > M 2 ). We also study the fate of the rapidly-rotating object which forms when two neutron stars merge. Although the object is stabilized by differential rotation, various secular processes destroy this support. Modeling these effects by a shear viscosity, we find that the merged remnant evolves into a uniformly rotating core, which in some cases collapses to a black hole, surrounded by a massive orbiting torus.
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