Numerical Simulations of Short Gamma-Ray Bursts

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The aim of this project is to simulate by numerical means the merging of compact objects involving a neutron star and a black hole in order to mimic the dynamics of short gamma-ray bursts. The physical interactions which need to be included in the simulations are manifold: self-gravity, hydrodynamic motion, neutrino emission and back-reaction, gravitational wave emission and back-reaction, micro-physical equation-of-state effects, nuclear reactions at high temperature and densities, and magnetic fields. These physical effects are reflected numerically and mathematically by diverse algorithms: elliptic equations are solved by fast-Fourier transforms, hyperbolic equations are solved on a nested grid in conservative form, large tables for the equation-of-state are interpolated tri-linearly, general relativistic effects are treated as post-Newtonian expansion, and the numerical code is parallelised in threads. A Fortran code will be provided to the student. This covers most of the effects mentioned above, but there are many avenues for improvement and more detailed analysis for the student to pursue, including but not restricted to: magnetic field effects, neutrino back-reaction, variants of equations-of-state, relativity both special and general. Should the student prefer to pursue a different direction there are freely available community codes available which could be adapted to this topic of investigation or the student could build on the alterations which previous PhD students have done in their theses.