Sonic surfaces for adiabatic flow in a stationary axisymmetric spacetime

Details Sonic surfaces for adiabatic flow in a stationary axisymmetric spacetime Sonic surfaces for adiabatic flow in a stationary axisymmetric spacetime

Jul 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989mnras.239...19a&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 239, July 1, 1989, p. 19-54.

Statistics

Computation

21

Adiabatic Flow, Computational Astrophysics, Relativistic Theory, Space-Time Functions, Parabolic Differential Equations, Polytropic Processes, Schwarzschild Metric

Scientific paper

The steady flow of a rotating adiabatic fluid in an axisymmetric stationary background spacetime is modeled using a quasi-linear second-order partial differential equation. The equation is shown to be parabolic if the flow is sonic. Under the assumption that the streamlines are orthogonal to the sonic surface, the total mass flux through the surface is found to be locally extremal, and the surface itself can be modeled using a fourth-order ordinary differential equation. Based on the knowledge of conditions in the flow at infinity, a simple theorem can determine the distribution of angular momentum on the sonic surface.

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