DescriptionKerr Newman De Sitter (KNdS) Horizons & Ergospheres.gif
English: The horizons and ergosheres for the Kerr Newman De Sitler (KNdS) spacetime with different Λ:M ratios. The mass M, spin a and electric charge ℧ of the black hole stay constant, as does the radius of the ring singularity (r=0 → R=√[r²+a²]=a), while the cosmological constant Λ=3H² is the animation parameter. All numbers are in natural dimensionless units of G=M=c=kₑ=1.
Snapshot 1 (a=0.9, ℧=0.4, Λ=0.109)Snapshot 2 (a=0.9, ℧=0.4, Λ=0.136)Orbit in the Kerr Newman De Sitter spacetimeSeparate depictions for the horizons and ergospheresRegular Kerr black hole (a=0.99, ℧=0, Λ=0)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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.
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 ).
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
↑ (2008). "Kerr-Newman-de Sitter black holes with a restricted repulsive barrier of equatorial photon motion". Physical Review D58: 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 Gravity40 (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 Gravitation46 (11): 1818. DOI:10.1007/s10714-014-1818-8.
↑ (2018). "Kerr-de Sitter spacetime, Penrose process and the generalized area theorem". Physical Review D97 (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 Gravity38 (4): 045018. DOI:10.1088/1361-6382/abd3e0.
↑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
Captions
Horizons and ergospheres for the Kerr Newman De Sitler spacetime