File:Kerr Newman De Sitter (KNdS) Ergospheres & Horizons.png
Kerr_Newman_De_Sitter_(KNdS)_Ergospheres_&_Horizons.png (620 × 464 pixels, file size: 58 KB, MIME type: image/png)
Captions
Contents
Summary edit
DescriptionKerr Newman De Sitter (KNdS) Ergospheres & Horizons.png |
English: The horizons and ergosheres for the Kerr Newman De Sitler (KNdS) spacetime with a high Λ:M ratio. |
Date | |
Source | Own work, Code: Link |
Author | Yukterez (Simon Tyran, Vienna) |
Other versions |
Licensing edit
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Overview edit
The Kerr–Newman–de–Sitter metric (KNdS) [1][2] is the one of the most general stationary solutions of the Einstein–Maxwell equations in [1] that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass embedded in an expanding universe. It generalizes the Kerr–Newman metric by taking into account the cosmological constant .
Boyer–Lindquist coordinates edit
In (+, −, −, −) signature and in natural units of the KNdS metric is[3][4][5][6]
with all the other , where is the black hole's spin parameter, its electric charge and [7] the cosmological constant with as the time-independent Sitter universe#Mathematical expression Hubble parameter. The electromagnetic 4-potential is
The frame-dragging angular velocity is
and the local frame-dragging velocity relative to constant positions (the speed of light at the ergosphere)
The escape velocity (the speed of light at the horizons) relative to the local corotating ZAMO (zero angular momentum observer) is
The conserved quantities in the equations of motion
where is the four velocity, is the test particle's specific charge and the Maxwell–Faraday tensor
are the total energy
and the covariant axial angular momentum
The for differentiation overdot stands for differentiation by the testparticle's proper time or the photon's affine parameter, so .
Null coordinates edit
To get coordinates we apply the transformation
and get the metric coefficients
and all the other , with the electromagnetic vector potential
Defining ingoing lightlike worldlines give a light cone on a spacetime diagram.
Horizons and ergospheres edit
The horizons are at and the ergospheres at . This can be solved numerically or analytically. Like in the Kerr and Kerr–Newman metrics the horizons have constant Boyer-Lindquist , while the ergospheres' radii also depend on the polar angle .
This gives 3 positive solutions each (including the black hole's inner and outer horizons and ergospheres as well as the cosmic ones) and a negative solution for the space at in the antiverse[8][9] behind the ring singularity, which is part of the probably unphysical extended solution of the metric.
With a negative (the Anti–de–Sitter variant with an attractive cosmological constant) there are no cosmic horizon and ergosphere, only the black hole related ones.
In the Nariai limit[10] the black hole's outer horizon and ergosphere coincide with the cosmic ones (in the Schwarzschild–de–Sitter metric to which the KNdS reduces with that would be the case when ).
Invariants edit
The Ricci scalar for the KNdS metric is , and the Kretschmann scalar
Further reading edit
For the transformation see here and the links therein. More tensors and scalars for the KNdS metric: in Boyer Lindquist and Null coordinates, higher resolution: video, advised references: arxiv:1710.00997 & arxiv:2007.04354. More snapshots of this series can be found here, those are also under the creative commons license.
References edit
- ↑ (2008). "Kerr-Newman-de Sitter black holes with a restricted repulsive barrier of equatorial photon motion". Physical Review D 58: 084003. DOI:10.1088/0264-9381/17/21/312.
- ↑ (2009). "Exact spacetimes in Einstein's General Relativity". Cambridge University Press, Cambridge Monographs in Mathematical Physics. DOI:10.1017/CBO9780511635397.
- ↑ (2023). "Motion equations in a Kerr-Newman-de Sitter spacetime". Classical and Quantum Gravity 40 (13). DOI:10.1088/1361-6382/accbfe.
- ↑ (2014). "Gravitational lensing and frame-dragging of light in the Kerr–Newman and the Kerr–Newman (anti) de Sitter black hole spacetimes". General Relativity and Gravitation 46 (11): 1818. DOI:10.1007/s10714-014-1818-8.
- ↑ (2018). "Kerr-de Sitter spacetime, Penrose process and the generalized area theorem". Physical Review D 97 (8): 084049. DOI:10.1103/PhysRevD.97.084049.
- ↑ (2021). "Null Hypersurfaces in Kerr-Newman-AdS Black Hole and Super-Entropic Black Hole Spacetimes". Classical and Quantum Gravity 38 (4): 045018. DOI:10.1088/1361-6382/abd3e0.
- ↑ Gaur & Visser: Black holes embedded in FLRW cosmologies (2023) class=gr-qc, arxiv eprint=2308.07374}}
- ↑ Andrew Hamilton: Black hole Penrose diagrams (JILA Colorado)
- ↑ Figure 2 in (2020). "Influence of Cosmic Repulsion and Magnetic Fields on Accretion Disks Rotating around Kerr Black Holes". Universe. DOI:10.3390/universe6020026.
- ↑ Leonard Susskind: Aspects of de Sitter Holography, timestamp 38:27: video of the online seminar on de Sitter space and Holography, Sept 14, 2021
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 00:05, 11 September 2023 | 620 × 464 (58 KB) | Yukterez (talk | contribs) | match the color of the cosmic ergosphere with the black hole one after they merged | |
22:30, 22 August 2023 | 620 × 464 (28 KB) | Yukterez (talk | contribs) | fit to the format of the other images | ||
20:12, 16 August 2023 | 640 × 464 (45 KB) | Yukterez (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 3 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Unique ID of original document | xmp.did:612f8e3c-d1b0-9b4f-b96f-31e7cc565cbb |
---|---|
Software used |