In an important series of articles published during the 1970s, Krasiński [Acta Phys. Pol. B 5, 411 (1974); 6, 223 (1975); J. Math. Phys. 16, 125 (1975); Rep. Math. Phys. 14, 225 (1978)] displayed a class of interior solutions of the Einstein field equations sourced by a stationary isentropic rotating cylinder of a perfect fluid. However, these solutions depend on an unspecified arbitrary function, which leads the author to claim that the equation of state of the fluid could not be obtained directly from the field equations but had to be added by hand. In the present article, we use a double ansatz, which we have developed in 2021 and implemented at length into a series of recent papers displaying exact interior solutions for a stationary rotating cylindrically symmetric fluid with anisotropic pressure. This ansatz allows us to obtain here a fully integrated class of solutions to the Einstein equations, written with the use of very simple analytical functions, and to show that the equation of state of the fluid follows naturally from these field equations.
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Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids
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February 2023
Research Article|
February 03 2023
Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids
M.-N. Célérier
M.-N. Célérier
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Supervision, Validation, Visualization, Writing – original draft)
Laboratoire Univers et Théories, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS
, F-92190 Meudon, France
a)Author to whom correspondence should be addressed: [email protected]
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a)Author to whom correspondence should be addressed: [email protected]
J. Math. Phys. 64, 022501 (2023)
Article history
Received:
October 25 2022
Accepted:
January 11 2023
Citation
M.-N. Célérier; Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids. J. Math. Phys. 1 February 2023; 64 (2): 022501. https://doi.org/10.1063/5.0131945
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