Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes
In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful conc...
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MDPI AG
2023-02-01
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| Online Access: | https://www.mdpi.com/2218-1997/9/3/120 |
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| author | Simen Braeck |
| author_facet | Simen Braeck |
| author_sort | Simen Braeck |
| collection | DOAJ |
| description | In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein’s equations for an approximate thin shell model, where we maintain a degree of freedom, by relaxing the natural assumption of vanishing rotation at asymptotic infinity, at the outset of the analysis. The solution reveals that Einstein’s equations only determine differences in the rotation rate of ZAMOs, thereby establishing the concept of relative rotation globally. The interpretation of rotation as relative in a global context is inherently linked to the freedom to transform between coordinate systems rotating relative to each other, implying that an arbitrary ZAMO located at any radius may claim to be the one that is non-rotating on a global scale, and that the notion of an asymptotic Lorentz frame relative to which one may measure absolute rotation is devoid of any meaning. The concept of rotation in Kerr spacetime is then briefly discussed in the context of this interpretation. |
| first_indexed | 2024-03-11T05:47:49Z |
| format | Article |
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| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-11T05:47:49Z |
| publishDate | 2023-02-01 |
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| spelling | doaj.art-1b3e479a9b1b4329bfa8c8150748a4b82023-11-17T14:15:44ZengMDPI AGUniverse2218-19972023-02-019312010.3390/universe9030120Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat SpacetimesSimen Braeck0Department of Computer Science, OsloMet—Oslo Metropolitan University, NO-0130 Oslo, NorwayIn axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein’s equations for an approximate thin shell model, where we maintain a degree of freedom, by relaxing the natural assumption of vanishing rotation at asymptotic infinity, at the outset of the analysis. The solution reveals that Einstein’s equations only determine differences in the rotation rate of ZAMOs, thereby establishing the concept of relative rotation globally. The interpretation of rotation as relative in a global context is inherently linked to the freedom to transform between coordinate systems rotating relative to each other, implying that an arbitrary ZAMO located at any radius may claim to be the one that is non-rotating on a global scale, and that the notion of an asymptotic Lorentz frame relative to which one may measure absolute rotation is devoid of any meaning. The concept of rotation in Kerr spacetime is then briefly discussed in the context of this interpretation.https://www.mdpi.com/2218-1997/9/3/120general relativityrotationrelative rotationinertial draggingframe draggingLense–Thirring effect |
| spellingShingle | Simen Braeck Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes Universe general relativity rotation relative rotation inertial dragging frame dragging Lense–Thirring effect |
| title | Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes |
| title_full | Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes |
| title_fullStr | Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes |
| title_full_unstemmed | Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes |
| title_short | Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes |
| title_sort | inertial frame dragging and relative rotation of zamos in axistationary asymptotically flat spacetimes |
| topic | general relativity rotation relative rotation inertial dragging frame dragging Lense–Thirring effect |
| url | https://www.mdpi.com/2218-1997/9/3/120 |
| work_keys_str_mv | AT simenbraeck inertialframedraggingandrelativerotationofzamosinaxistationaryasymptoticallyflatspacetimes |