Internal and external metrics for a perfect fluid cylinder in general relativity

Journal Article · Wed Aug 01 00:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.529021· OSTI ID:6692372

Davidson, W ^[1]

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1. Mathematics Department, University of Otago, Dunedin (New Zealand)

A solution to Einstein's equations describing a perfect fluid cylinder of finite radius is presented. The proper density {mu} and pressure {ital p} of the fluid are physically well behaved in the radial coordinate range 0{le}{ital r}{le}{ital r}{sub 1}. On the axis ({ital r}=0) the solution is regular and {mu} and {ital p} are finite and positive. As {ital r} increases {mu} and {ital p} decrease steadily through positive values, {ital p} vanishing at {ital r}={ital r}{sub 1}. The ratio {ital p}/{mu} ({lt}1) is also monotonically decreasing, as is also the velocity of sound {ital a} ({lt}1) in the fluid. The equation of state is {ital p}= (3)/(7) {mu}{minus}{ital N}{mu}{sup 3/10}, where {ital N} is a positive constant. The matching metric for the vacuum exterior to the cylinder is given, so that the space-time is complete and nonsingular.

• OSTI ID: 6692372
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:8; ISSN 0022-2488; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
CYLINDERS
DENSITY
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF STATE
FIELD EQUATIONS
FIELD THEORIES
FLUIDS
GENERAL RELATIVITY THEORY
METRICS
PHYSICAL PROPERTIES
PRESSURE GRADIENTS
SINGULARITY
SOUND WAVES
SPACE-TIME
STEADY-STATE CONDITIONS
VELOCITY