Publikace ÚTF

Thin disks as sources of stationary axisymmetric electrovacuum spacetimes

Tomáš Ledvinka

For a wide class of stationary axially symmetric electro-vacuum spacetimes we show a possibility to construct disk-like "interior solutions". These sources provide nice illustration of the well known fact that the Einstein equations govern not only the behavior of the gravitational field but also yield equations of motion for the matter. Thus, if a stress-energy tensor with a non-negative azimuthal and vanishing radial pressure is obtained by a removal of the equatorial region of spacetime considered, and two counter-rotating circular geodesics exist in the plane of the disk, the disk may be formed by assigning appropriate energy and charge densities to both counter-rotating streams. It is generally observed that such interpretation is allowed as long as the width of the excluded region is large enough. If the effective radius of the disk is small, it is not possible to construct disks with large a/M. The disks with smaller a/M can be highly relativistic, their central redshifts can be arbitrarily large. In the astrophysically most plausible models, around 90% of the total mass of the disk of dust is rotating in one direction along geodesics and only 10% of the mass moves along counter-rotating geodesics.
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