Harrison transformation of hyperelliptic solutions and charged dust disks

Details Harrison transformation of hyperelliptic solutions and charged dust disks Harrison transformation of hyperelliptic solutions and charged dust disks

2005-12-22

arxiv.org/abs/gr-qc/0512133v1

Phys.Rev. D65 (2002) 084029

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 9 figures

Scientific paper

10.1103/PhysRevD.65.084029

We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail. Analytic expressions for the metric and the multipole moments are obtained. As an example we consider the transformation of a family of counter-rotating dust disks. The resulting solutions can be interpreted as disks with currents and matter with a purely azimuthal pressure or as two streams of freely moving charged particles. We discuss interesting limiting cases as the extreme limit where the charge becomes identical to the mass, and the ultrarelativistic limit where the central redshift diverges.

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