A semi-tetrad decomposition of the Kerr spacetime
Abstract In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the horizon. Comparisons are drawn between an observer belonging to the Killing frame and a ZAMO (zero angular mome...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-04-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11433-x |
| _version_ | 1797822703752708096 |
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| author | C. Hansraj R. Goswami S. D. Maharaj |
| author_facet | C. Hansraj R. Goswami S. D. Maharaj |
| author_sort | C. Hansraj |
| collection | DOAJ |
| description | Abstract In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the horizon. Comparisons are drawn between an observer belonging to the Killing frame and a ZAMO (zero angular momentum observer), a locally non-rotating observer in a zero angular momentum frame, and their resulting geometrical quantities that generate the evolution and propagation equations. This enhances the study of the Kerr geometry as the results are valid in the ergoregion from where energy can be extracted. Using this formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner not present in alternate approaches. We find significant relationships between the properties of shear, vorticity and acceleration. Additionally we observe that in the Killing frame, the gravitational wave is a direct consequence of vorticity and in the ZAMO frame, the gravitational wave is a direct consequence of shear. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach, and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime. |
| first_indexed | 2024-03-13T10:13:03Z |
| format | Article |
| id | doaj.art-e998c1dcc2b9462b85ff6c19d386a692 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-13T10:13:03Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-e998c1dcc2b9462b85ff6c19d386a6922023-05-21T11:24:35ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-04-0183411510.1140/epjc/s10052-023-11433-xA semi-tetrad decomposition of the Kerr spacetimeC. Hansraj0R. Goswami1S. D. Maharaj2Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-NatalAstrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-NatalAstrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-NatalAbstract In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the horizon. Comparisons are drawn between an observer belonging to the Killing frame and a ZAMO (zero angular momentum observer), a locally non-rotating observer in a zero angular momentum frame, and their resulting geometrical quantities that generate the evolution and propagation equations. This enhances the study of the Kerr geometry as the results are valid in the ergoregion from where energy can be extracted. Using this formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner not present in alternate approaches. We find significant relationships between the properties of shear, vorticity and acceleration. Additionally we observe that in the Killing frame, the gravitational wave is a direct consequence of vorticity and in the ZAMO frame, the gravitational wave is a direct consequence of shear. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach, and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.https://doi.org/10.1140/epjc/s10052-023-11433-x |
| spellingShingle | C. Hansraj R. Goswami S. D. Maharaj A semi-tetrad decomposition of the Kerr spacetime European Physical Journal C: Particles and Fields |
| title | A semi-tetrad decomposition of the Kerr spacetime |
| title_full | A semi-tetrad decomposition of the Kerr spacetime |
| title_fullStr | A semi-tetrad decomposition of the Kerr spacetime |
| title_full_unstemmed | A semi-tetrad decomposition of the Kerr spacetime |
| title_short | A semi-tetrad decomposition of the Kerr spacetime |
| title_sort | semi tetrad decomposition of the kerr spacetime |
| url | https://doi.org/10.1140/epjc/s10052-023-11433-x |
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