Abstract
We discuss the Price’s theorem in the context of newly established exact solutions of static and non-static distorted black holes. Some numerics are given in “pro et contra” of their consideration in problems of astrophysics and Gauge/Gravity duality. Our analysis leads to a remarkable quantitative agreement between the relaxation time of AdS small black holes and lifetime of the Quark–Gluon plasma that gives another evidence to apply black hole physics to the description of strongly coupled relativistic fluids.
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Notes
Note that the rigorous mathematical proof of the “no-hair” theorem is still missing. But would it be regained it were dealt with solely mathematical black holes.
There are many pitfalls on this way. In practice, the observation of the gravitational wave flow requires a good intensity of the signal first; and second, its frequency has to fall within the bandwidth of the gravitational waves interferometers (the ground based A-LIGO or the planning space based eLISA). The bandwidth of the planning eLISA interferometer (see [30] for details in this respect) is well to catch the oscillations from the SMBH Sgr A* in the centre of our Galaxy with mass \(M \sim 3.7 \times {{10}^{6}}{{M}_{ \odot }}.\) (The oscillations frequency ν in [30] is related to our ω in (3) as \(\nu = {\omega \mathord{\left/ {\vphantom {\omega {2\pi }}} \right. \kern-0em} {2\pi }}.\)) But one should have in mind the constant gravitational wave’s flow (a gravitational “noise”) from the Sgr A* due to the BH accretion disk, intensity of which is larger than that of the BH horizon rearrangement. Independent data from another type detector such as, for example, the Event Horizon Telescope, may improve the situation and can be used as a cross-check.
The early discussion on the role of the small BHs in the AdS/CFT can be found in [34].
The horizon location of the AdS-Schwarzschild BH is determined by \({{r}_{ + }} = \max \{ r,f(r) = {{(\kappa r)}^{2}} - {{2M} \mathord{\left/ {\vphantom {{2M} r}} \right. \kern-0em} r} + 1 = 0\} \) that, on account of the small BH condition \({{(\kappa {{r}_{ + }})}^{2}} \ll 1\) with the inverse characteristic length of the AdS4 space κ, becomes almost the same as for the Minkowski neutral BH.
REFERENCES
S. A. Hughes, “Trust but verify: The Case for astrophysical black holes,” eConf. C 0507252, L006 (2005), arXiv:hep-ph/0511217.
The Galactic Black Holes, Ed. by H. Falcke and F. W. Hehl, IOP Bristol and Philadelphia, 2003.
A. Fabbri and J. Navarro-Salas, Modelling Black Hole Evaporation (Imperial Colledge Press, London, 2005).
W. G. Unruh and R. M. Wald, “Information loss,” Rep. Prog. Phys. 80, 092002 (2017).
F. Haardt et al., Astrophysical Black Holes, Lecture Notes in Physics, Vol. 905, Springer-Verlag, 2016.
T. Johannsen, Sgr A* and General Relativity, arXiv:1512.03818[astro-ph.GA].
H. Stephani, D. Kramer, M. MacCallum, C. Honselaers, and E. Herlt, Exact Solutions of Einstein Field Equations (Cambridge University Press, 2003).
J. B. Griffiths and J. Podolsky, Exact Space-Times in Einstein’s General Relativity (Cambridge University Press, 2012).
N. Gürlebeck, “No-hair theorem for Black Holes in astrophysical environments,” Phys. Rev. Lett. 114, 151102 (2015).
R. H. Price, “Nonspherical perturbations of relativistic gravitational collapse. 1. Scalar and gravitational perturbations,” Phys. Rev. D 5, 2419 (1972).
R. H. Price, “Nonspherical perturbations of relativistic gravitational collapse. II. Integer-spin, zero-rest-mass fields,” Phys. Rev. D 5, 2439 (1972).
W. Israel, “Event Horizons in static vacuum space-times,” Phys. Rev. 164, 1776 (1967).
R. Geroch and J. B. Hartle, “Distorted black holes,” J. Math. Phys. 23, 680 (1982).
H. Weyl, “Zur Gravitationstheorie,” Ann. Phys. 54, 117 (1917).
K. S. Thorne, “Nonspherical gravitational collapse: Does it produce Black Holes?,” Comments Astrophys. Space Phys. 2, 191 (1970).
K. S. Thorne, “Nonspherical gravitational collapse: A short review,” in Magic Without Magic, Ed. by J. R. Klauder (San Francisco, 1972), pp. 231–258.
M. Ammon and J. Erdmenger, Gauge/Gravity Duality: Foundations and Applications (Cambridge University Press, 2015).
M. Natsuume, “AdS/CFT duality user guide,” in Lecture Notes in Physics, Vol. 903 (Springer, Japan, 2015).
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions (Cambridge University Press, 2014).
T. Moskalets and A. Nurmagambetov, “Liouville mode in gauge/gravity duality,” Eur. Phys. J. C 75, 551 (2015).
T. M. Moskalets and A. J. Nurmagambetov, “Non-uniform horizons in gauge/gravity duality,” Phys. At. Nucl. 79, 1497 (2016).
T. Moskalets and A. Nurmagambetov, Absorption cross-sections of small quasi-spherical black holes: The massless scalar case, arXiv:1607.08830[gr-qc].
T. M. Moskalets and A. J. Nurmagambetov, “Static and non-static black holes with the Liouville mode,” Phys. Part. Nucl. Lett. 14, 365 (2017).
J. W.York, Jr., “Dynamical origin of Black Hole radiance,” Phys. Rev. D 28, 2929 (1983).
S. Chandrasekhar and S. L. Detweiler, “The quasi-normal modes of the Schwarzschild black hole,” Proc. R. Soc. London, Ser. A 344, 441 (1975).
H. T. Cho, A. S. Cornell, J. Doukas, T. R. Huang, and W. Naylor, “A new approach to Black Hole quasinormal modes: A review of the asymptotic iteration method,” Adv. Math. Phys. 2012, 281705 (2012).
S. Iyer and C. M. Will, “Black Hole normal modes: A WKB approach. 1. Foundations and application of a higher order WKB analysis of potential barrier scattering,” Phys. Rev. D 35, 3621 (1987).
S. Iyer, “Black Hole normal modes: A WKB approach. 2. Schwarzschild Black Holes,” Phys. Rev. D 35, 3632 (1987).
G. Siopsis, “Analytic calculation of quasi-normal modes,” in Lecture in Notes Physics, Vol. 769 (Springer, 2009), p. 471.
V. Ferrari and L. Gualtieri, “Quasi-normal modes and gravitational wave astronomy,” Gen. Rel. Grav. 40, 945 (2008).
J. Dexter and E. Agol, “Quasar accretion disks are strongly inhomogeneous,” Astrophys. J. 727, L24 (2011).
J. Dexter and E. Quataert, “Inhomogeneous accretion discs and the soft states of black hole X-ray binaries,” Mon. Not. R. Astron. Soc. 426, 71 (2012).
A. Ricarte and J. Dexter, “The Event Horizon Telescope: Exploring strong gravity and accretion physics,” Mon. Not. R. Astron. Soc. 446, 1973 (2015).
G. T. Horowitz and V. E. Hubeny, “Quasinormal modes of AdS black holes and the approach to thermal equilibrium,” Phys. Rev. D 62, 024027 (2000).
K. D. Kokkotas and B. G. Schmidt, “Quasinormal modes of stars and black holes,” Living Rev. Rel. 2, 2 (1999).
K. S. Thorne, “Multipole expansions of gravitational radiation,” Rev. Mod. Phys. 52, 299 (1980).
V. Cardoso, R. Konoplya, and J. P. S. Lemos, “Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter space-times: A complete study on the asymptotic behavior,” Phys. Rev. D 68, 044024 (2003).
T. A. Moore, A General Relativity Workbook (Univ. Science Books, 2012).
V. Khachatryan et al. (CMS Collab.), “Evidence for collective multiparticle correlations in \(p\)-Pb collisions,” Phys. Rev. Lett. 115, 012301 (2015).
M. Martin-Neira et al., “Space-borne radio telescope to image the supermassive black hole at our galactic centre,” in Proceedings of the 38th ESA Antenna Workshop, ESA/ESTEC (Netherlands, 2017).
ACKNOWLEDGMENTS
AJN thanks to the Organisers and participants of the SQS’17 meeting for nice atmosphere during the event. Work supported in part by Ministry of Education and Science of Ukraine.
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Arslanaliev, A.M., Nurmagambetov, A.J. Price’s Theorem in Gauge/Gravity Duality. Phys. Part. Nuclei 49, 879–883 (2018). https://doi.org/10.1134/S1063779618050039
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DOI: https://doi.org/10.1134/S1063779618050039