Version 1
: Received: 30 October 2023 / Approved: 30 October 2023 / Online: 31 October 2023 (05:19:32 CET)
How to cite:
Arslanaliev, A.M.; Nurmagambetov, A.J. Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach. Preprints2023, 2023101940. https://doi.org/10.20944/preprints202310.1940.v1
Arslanaliev, A.M.; Nurmagambetov, A.J. Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach. Preprints 2023, 2023101940. https://doi.org/10.20944/preprints202310.1940.v1
Arslanaliev, A.M.; Nurmagambetov, A.J. Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach. Preprints2023, 2023101940. https://doi.org/10.20944/preprints202310.1940.v1
APA Style
Arslanaliev, A.M., & Nurmagambetov, A.J. (2023). Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach. Preprints. https://doi.org/10.20944/preprints202310.1940.v1
Chicago/Turabian Style
Arslanaliev, A.M. and A. J. Nurmagambetov. 2023 "Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach" Preprints. https://doi.org/10.20944/preprints202310.1940.v1
Abstract
We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the (projected) Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include logarithmic derivarives of a parameter (the regularization function) determining the proximity of a stretched membrane to the BH horizon. Direct computation of the new terms for exact (Schwarzschild and Kerr) solutions to the Einstein equations results in vanishing the additions to the RDNS equations in the horizon limit. For spacetimes, which are not exact solutions to the Einstein equations, as, for instance, for space-time configurations mimicking black holes, taking into account new terms in the RDNS equations is the mandatory operation. We also comment the correspondence between the horizon limit of the Parikh-Wilczek Membrane Approach and the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as the link of the obtained results to our previous work on the Kerr black holes.
Keywords
Black Holes; Membrane Paradigm; Relativistic Hydrodynamics
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
