Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Shear-free perfect fluid theorems in general relativity
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 pac...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2023
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613160900395008 |
|---|---|
| access_status_str | Open Access |
| author | Sikhonde, Muzikayise Edward |
| author2 | Dunsby, Peter Klaus |
| author_browse | Dunsby, Peter Klaus Sikhonde, Muzikayise Edward |
| author_facet | Dunsby, Peter Klaus Sikhonde, Muzikayise Edward |
| author_sort | Sikhonde, Muzikayise Edward |
| collection | Thesis |
| description | 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 |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/38542 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:43.046Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/38542 Shear-free perfect fluid theorems in general relativity Sikhonde, Muzikayise Edward Dunsby, Peter Klaus Ellis George Fluid Theorems 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 2023-09-12T08:26:49Z 2023-09-12T08:26:49Z 2023 2023-09-12T08:26:20Z Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/38542 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Fluid Theorems Sikhonde, Muzikayise Edward Shear-free perfect fluid theorems in general relativity |
| thesis_degree_str | Doctoral |
| title | Shear-free perfect fluid theorems in general relativity |
| title_full | Shear-free perfect fluid theorems in general relativity |
| title_fullStr | Shear-free perfect fluid theorems in general relativity |
| title_full_unstemmed | Shear-free perfect fluid theorems in general relativity |
| title_short | Shear-free perfect fluid theorems in general relativity |
| title_sort | shear free perfect fluid theorems in general relativity |
| topic | Fluid Theorems |
| url | http://hdl.handle.net/11427/38542 |
| work_keys_str_mv | AT sikhondemuzikayiseedward shearfreeperfectfluidtheoremsingeneralrelativity |