{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/38542"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/38542","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Shear-free perfect fluid theorems in general relativity","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","abstract_html":"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","abstract_has_math":false,"creators":["Sikhonde, Muzikayise Edward"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Dunsby, Peter Klaus","Ellis George"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-22T22:22:38Z","subjects":["Fluid Theorems"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/38542","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dunsby, Peter Klaus","Ellis George"]},{"key":"dc:creator","label":"Author","values":["Sikhonde, Muzikayise Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-09-12T08:26:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-09-12T08:26:49Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral","PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Fluid Theorems"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/38542"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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"]},{"key":"dc:title","label":"Title","values":["Shear-free perfect fluid theorems in general relativity"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dunsby, Peter Klaus","Ellis George"],"dc:creator":["Sikhonde, Muzikayise Edward"],"dc:date.accessioned":["2023-09-12T08:26:49Z"],"dc:date.available":["2023-09-12T08:26:49Z"],"dc:date.issued":["2023"],"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.uri":["http://hdl.handle.net/11427/38542"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Fluid Theorems"],"dc:title":["Shear-free perfect fluid theorems in general relativity"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral","PhD"]},"updated_at":"2026-07-22T22:22:38Z"}