### Abstract

Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the stationary Killing field are functionally independent. It has been pointed out earlier by one of us (IR) that for these perfect-fluid geometries some of the basic field equations are invariant under an SL(2, ℝ) transformation. Here it is shown that this transformation can be applied to generate possibly new perfect-fluid solutions from existing known ones only for the case of a barotropic equation of state ρ + 3p = 0. In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions could be written in a singe compact form. A new derivation of all Petrov type D stationary axisymmetric rigidly-rotating perfect-fluid solutions with an equation of state ρ + 3p = constant is given in an appendix.

Original language | English |
---|---|

Pages (from-to) | 2783-2795 |

Number of pages | 13 |

Journal | Classical and Quantum Gravity |

Volume | 13 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Classical and Quantum Gravity*,

*13*(10), 2783-2795. https://doi.org/10.1088/0264-9381/13/10/015

**Generating new perfect-fluid solutions from known ones.** / Rácz, I.; Zsigrai, József.

Research output: Contribution to journal › Article

*Classical and Quantum Gravity*, vol. 13, no. 10, pp. 2783-2795. https://doi.org/10.1088/0264-9381/13/10/015

}

TY - JOUR

T1 - Generating new perfect-fluid solutions from known ones

AU - Rácz, I.

AU - Zsigrai, József

PY - 1996

Y1 - 1996

N2 - Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the stationary Killing field are functionally independent. It has been pointed out earlier by one of us (IR) that for these perfect-fluid geometries some of the basic field equations are invariant under an SL(2, ℝ) transformation. Here it is shown that this transformation can be applied to generate possibly new perfect-fluid solutions from existing known ones only for the case of a barotropic equation of state ρ + 3p = 0. In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions could be written in a singe compact form. A new derivation of all Petrov type D stationary axisymmetric rigidly-rotating perfect-fluid solutions with an equation of state ρ + 3p = constant is given in an appendix.

AB - Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the stationary Killing field are functionally independent. It has been pointed out earlier by one of us (IR) that for these perfect-fluid geometries some of the basic field equations are invariant under an SL(2, ℝ) transformation. Here it is shown that this transformation can be applied to generate possibly new perfect-fluid solutions from existing known ones only for the case of a barotropic equation of state ρ + 3p = 0. In order to study the effect of this transformation, its application to known perfect-fluid solutions is presented. In this way, different previously known solutions could be written in a singe compact form. A new derivation of all Petrov type D stationary axisymmetric rigidly-rotating perfect-fluid solutions with an equation of state ρ + 3p = constant is given in an appendix.

UR - http://www.scopus.com/inward/record.url?scp=21444438155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21444438155&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/13/10/015

DO - 10.1088/0264-9381/13/10/015

M3 - Article

AN - SCOPUS:21444438155

VL - 13

SP - 2783

EP - 2795

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 10

ER -