Numerical solution to the Einstein-Maxwell equations of a rotating disc of charged dust
In this work, the numerical solution of the Einstein-Maxwell equations of a rotating disc of charged dust and the extended application of its solution results are presented. The formation of the field equations for the rotating charged fluid are discussed. The boundary conditions, which provide the disc character, are derived subsequently from the field equations. Combining the field equations and the boundary conditions yields an equation system describing a rotating disc of charged dust, which is in turn solved by the numerical approach of the pseudo-spectral method. Further discussion of the improvement on the calculation speed, such as the analytical mesh-refinement is also included. The outcome raw potential data of the equation system is processed into more straightforward and intuitive physical quantities, which can further be utilised to analyse the gyromagnetic character of the system. Furthermore, the ergosphere surface can be obtained by analysing the raw data using the bisection method. All the results are summarised in the final chapters of this work. The discussion covers the whole parameter space: from the classical limit to the black hole limit, and from the non-charged limit to the electrical counter-poised limit. A detailed discussion of the gyromagnetic factor and different methods of its acquisition are compared. The configuration of the ergosphere surface is presented, as observed from both the near-source and far-field perspectives. A complete survey from the point at which the ergosphere starts appearing is discussed, covering the whole parameter space. Possible further development of this work is also discussed in the final chapter.
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