Study of a family of stationary and axially symmetric differentially rotating perfect fluids

Details Study of a family of stationary and axially symmetric differentially rotating perfect fluids Study of a family of stationary and axially symmetric differentially rotating perfect fluids

Nov 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996phrvd..54.6166m&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 54, Issue 10, 15 November 1996, pp.6166-6180

Mathematics

Logic

5

Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields, Exact Solutions

Scientific paper

The geometrical analysis and interpretation of a family of stationary and axisymmetric differentially rotating perfect fluids is performed. The family was first found by Senovilla and later by Mars and Senovilla under completely different hypotheses, and contains an arbitrary function of a single coordinate so there exists a large variety of behaviors. We find under which conditions the spacetime is axially symmetric with a well-defined axis of symmetry and when it satisfies the energy conditions. By imposing the reasonable assumption that the rotating body is finite in size we find two geometrically different classes of spacetimes. One of them represents a topological three-sphere with special properties. The other class is very interesting from the physical point of view, as it typically represents an isolated compact body with axial symmetry (with or without equatorial symmetry), and possible pointlike singularities at the north and south poles. There are even exotic examples in this class, as these objects can contain central and/or toroidal empty holes. As far as we know, these models are the more realistic explicit solutions produced so far by Einstein's theory in order to describe the interior of axially symmetric differentially rotating isolated compact bodies.

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