## Shear-free perfect fluid theorems in general relativity

dc.contributor.advisor | Dunsby, Peter Klaus | |

dc.contributor.advisor | Ellis George | |

dc.contributor.author | Sikhonde, Muzikayise Edward | |

dc.date.accessioned | 2023-09-12T08:26:49Z | |

dc.date.available | 2023-09-12T08:26:49Z | |

dc.date.issued | 2023 | |

dc.date.updated | 2023-09-12T08:26:20Z | |

dc.description.abstract | We present a detailed method for proving shear-free perfect fluid theorems in General Relativity. This method uses the (1+3)-covariant formalism to establish the consistency of the Einstein gravitational field equations under the barotropic shear-free perfect fluid condition. Using a Mathematica package xTensor, we were able to prove the following cases: the case where the pressure is constant, the acceleration vector is parallel to the vorticity, the components of a rescaled acceleration vector field orthogonal to the vorticity are basic and the case where the dot product of the rescaled acceleration vector field and the unit vorticity vector is basic, leading to the existence of a Killing vector along the vorticity | |

dc.identifier.apacitation | Sikhonde, M. E. (2023). <i>Shear-free perfect fluid theorems in general relativity</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/38542 | en_ZA |

dc.identifier.chicagocitation | Sikhonde, Muzikayise Edward. <i>"Shear-free perfect fluid theorems in general relativity."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023. http://hdl.handle.net/11427/38542 | en_ZA |

dc.identifier.citation | Sikhonde, M.E. 2023. Shear-free perfect fluid theorems in general relativity. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/38542 | en_ZA |

dc.identifier.ris | TY - Doctoral Thesis AU - Sikhonde, Muzikayise Edward AB - We present a detailed method for proving shear-free perfect fluid theorems in General Relativity. This method uses the (1+3)-covariant formalism to establish the consistency of the Einstein gravitational field equations under the barotropic shear-free perfect fluid condition. Using a Mathematica package xTensor, we were able to prove the following cases: the case where the pressure is constant, the acceleration vector is parallel to the vorticity, the components of a rescaled acceleration vector field orthogonal to the vorticity are basic and the case where the dot product of the rescaled acceleration vector field and the unit vorticity vector is basic, leading to the existence of a Killing vector along the vorticity DA - 2023 DB - OpenUCT DP - University of Cape Town KW - Fluid Theorems LK - https://open.uct.ac.za PY - 2023 T1 - Shear-free perfect fluid theorems in general relativity TI - Shear-free perfect fluid theorems in general relativity UR - http://hdl.handle.net/11427/38542 ER - | en_ZA |

dc.identifier.uri | http://hdl.handle.net/11427/38542 | |

dc.identifier.vancouvercitation | Sikhonde ME. Shear-free perfect fluid theorems in general relativity. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/38542 | en_ZA |

dc.language.rfc3066 | eng | |

dc.publisher.department | Department of Mathematics and Applied Mathematics | |

dc.publisher.faculty | Faculty of Science | |

dc.subject | Fluid Theorems | |

dc.title | Shear-free perfect fluid theorems in general relativity | |

dc.type | Doctoral Thesis | |

dc.type.qualificationlevel | Doctoral | |

dc.type.qualificationlevel | PhD |