Complex frequencies of a massless scalar field in loop quantum black hole spacetime

doi:10.1088/1674-1056/20/3/030401

Abstract Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole (LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner--Nordström black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a₀ causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.

Keywords: complex frequencies massless scalar field loop quantum black hole spacetime

Received: 23 July 2010
Revised: 19 August 2010
Accepted manuscript online:

PACS:	04.20.-q	(Classical general relativity)
	04.80.-y	(Experimental studies of gravity)

Fund: Project supported Project supported by the National Natural Science Foundation of China (Grant No. 10873004), the Program for Excellent Talents at Hunan Normal University, China, the National Basic Research Program of China (Grant No. 2010CB832803), the Key Program of the National Natural Science Foundation of China (Grant No. 10935013), the Construct Program of the National Key Discipline, and the Program for Changjiang Scholars and the Innovative Research Team in University, China (Grant No. IRT0964).

Cite this article:

Chen Ju-Hua(陈菊华) and Wang Yong-Jiu(王永久) Complex frequencies of a massless scalar field in loop quantum black hole spacetime 2011 Chin. Phys. B 20 030401

[1]	Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
[2]	Ashtekar A and Lewandowski J 2004 Class. Quant. Grav. 21 R53
[3]	Han M X, Huang W M and Ma Y G 2007 Int. J. Mod. Phys. D 16 1397
[4]	Han M X and Ma Y G 2006 Class. Quant. Grav. 23 2741
[5]	Bojowald M 2001 Phys. Rev. Lett. 86 5227
[6]	Ashtekar A, Pawlowski T, Singh P and Vandersloot K 2007 Phys. Rev. D 75 024035
[7]	Modesto L 2004 Phys. Rev. D 70 124009
[8]	Ashtekar A and Bojowald M 2006 Class. Quant. Grav. 23 391
[9]	Modesto L 2006 Class. Quant. Grav. 23 5587
[10]	Modesto L 2010 Int. J. Theor. Phys. arXiv:0811.2196 [gr-qc]
[11]	Modesto L 2006 Class. Quant. Grav. 23 5587
[12]	Hossenfelder S, Modesto L and Pr'emont-Schwarz I 2010 Phys. Rev. D 81 044036
[13]	Campiglia M, Gambini R and Pullin J 2007 Class. Quant. Grav. 24 3649
[14]	Konoplya R A 2003 Phys. Rev. D 68 024018
[15]	Maggiore M 2008 Phys. Rev. Lett. 100 141301
[16]	Hod S 1998 Phys. Rev. Lett. 81 4293
[17]	Dreyer O 2003 Phys. Rev. Lett. 90 081301
[18]	Maldacena J 1998 Adv. Theor. Math. Phys. 2 231
[19]	Witten E 1998 Adv. Theor. Math. Phys. 2 253
[20]	Morgan J, Cardoso V, Miranda A S, Molina C and Zanchin V T 2009 Phys. Rev. D 80 024024
[21]	Alsup J and Siopsis G 2008 Phys. Rev. D 78 086001
[22]	Cardoso V, Konoplya R and Lemos J P 2003 Phys. Rev. D 68 044024
[23]	Jing J L and Pan Q Y 2005 Nucl. Phys. B 728 109
[24]	Jing J L 2005 Phys. Rev. D 71 124006
[25]	Giammatteo M and Jing J L 2005 Phys. Rev. D 71 024007
[26]	Wang B, Lin C Y and Molina C 2004 Phys. Rev. D 70 064025
[27]	Du D P, Wang B and Su R K 2004 Phys. Rev. D 70 064024
[28]	Ma C R, Gui Y X, Wang W and Wang F J 2006 arXiv: 0611146[gr-qc]
[29]	Chakrabarti S K 2007 Gen. Rel. Grav. 39 567
[30]	He X, Wang B, Wu S F and Lin C Y 2009 Phys. Lett. B 673 156
[31]	Yun S M, Kim Y W and Park Y J 2008 Eur. Phys. J. C 58 617
[32]	Chen S B and Jing J L 2005 Class. Quant. Grav. 22 4651
[33]	Zhang Y, Gui Y X, Yu F and Li F L 2007 Gen. Rel. Grav. bf39 1003
[34]	Zhang Y and Gui Y X 2006 Class. Quant. Grav. 23 6141
[35]	Xi P 2009 Astrophys. Space Sci. 321 47
[36]	Zhang Y, Gui Y X and Yu F 2009 Chin. Phys. Lett. 26 030401
[37]	Chen J H and Wang Y J 2010 Int. J. Mod. Phys. A 25 1439
[38]	Chen J H and Wang Y J 2003 Class. Quantum. Grav. 20 3897
[39]	Chen J H and Wang Y J 2008 Chin. Phys. B 17 1184
[40]	Chen J H and Wang Y J 2006 Chin. Phys. 15 1705
[41]	Chen J H and Wang Y J 2007 Chin. Phys. 16 3212
[42]	Chen J H and Wang Y J 2010 Chin. Phys. B 19 010401
[43]	Chen J H and Wang Y J 2010 Chin. Phys. B 19 060401
[44]	L'opez-Ortega A 2009 Int. J. Mod. Phys. D 18 1441
[45]	Chakrabarti S K 2009 Eur. Phys. J. C 61 477
[46]	Kao H C and Tomino D 2008 Phys. Rev. D bf77 127503
[47]	Cardoso V, Lemos J P S and Yoshida S 2004 Phys. Rev. D 69 044004
[48]	Cardoso V, Lemos J P S and Yoshida S 2003 JHEP 0312 004
[49]	Jing J L 2005 JHEP 0512 005
[50]	Shu F W and Shen Y G 2005 Phys. Lett. B 614 195
[51]	Berti E and Kokkotas K D 2003 Phys. Rev. D 67 064020
[52]	Brown E, Mann R and Modesto L 2010 arXiv: 1006.4164 [gr-qc]
[53]	Schutz B F and Will C M 1985 Astrophys. J. Lett. 291 L33
[54]	Iyer S and Will C M 1987 Phys. Rev. D 35 3621
[55]	Iyer S 1987 Phys. Rev. D 35 3632

[1]	Laboratory demonstration of geopotential measurement using transportable optical clocks Dao-Xin Liu(刘道信), Jian Cao(曹健), Jin-Bo Yuan(袁金波), Kai-Feng Cui(崔凯枫), Yi Yuan(袁易),Ping Zhang(张平), Si-Jia Chao(晁思嘉), Hua-Lin Shu(舒华林), and Xue-Ren Huang(黄学人). Chin. Phys. B, 2023, 32(1): 010601.
[2]	Gravitation induced shrinkage of Mercury’s orbit Moxian Qian(钱莫闲), Xibin Li(李喜彬), and Yongjun Cao(曹永军)†. Chin. Phys. B, 2020, 29(10): 109501.
[3]	Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure Xin-Yun Hu(胡馨匀), Ke-Jian He(何柯健), Zhong-Hua Li(李中华), Guo-Ping Li(李国平). Chin. Phys. B, 2020, 29(5): 050401.
[4]	The global monopole spacetime and its topological charge Hongwei Tan(谭鸿威), Jinbo Yang(杨锦波), Jingyi Zhang(张靖仪), Tangmei He(何唐梅). Chin. Phys. B, 2018, 27(3): 030401.
[5]	A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism Yi-De Jing(景艺德), Jun-Jin Peng(彭俊金). Chin. Phys. B, 2017, 26(10): 100401.
[6]	Solution of Dirac equation around a charged rotating black hole Lü Yan (吕嫣), Hua Wei (花巍). Chin. Phys. B, 2014, 23(4): 040403.
[7]	The stability of a shearing viscous star with an electromagnetic field M. Sharif, M. Azama. Chin. Phys. B, 2013, 22(5): 050401.
[8]	Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity Gamal G.L. Nashed . Chin. Phys. B, 2012, 21(3): 030401.
[9]	Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism Gamal G.L. Nashed . Chin. Phys. B, 2012, 21(1): 010401.
[10]	Energy and spatial momentum of charged rotating frames in tetrad gravity Gamal G.L. Nashed . Chin. Phys. B, 2011, 20(11): 110401.
[11]	Thermodynamic and geometric framework of a (2+1)-dimensional black hole with non-linear electrodynamics Chen Gang(陈刚), Liu Zhan-Fang(刘占芳), and Lan Ming-Jian(兰明建) . Chin. Phys. B, 2011, 20(11): 110404.
[12]	Time-like geodesic structure of a spherically symmetric black hole in the brane-world Zhou Sheng(周盛), Chen Ju-Hua(陈菊华), and Wang Yong-Jiu(王永久) . Chin. Phys. B, 2011, 20(10): 100401.
[13]	Energy and momentum of rotating frames in tetrad gravity Gamal G L Nashed . Chin. Phys. B, 2011, 20(10): 100402.
[14]	A note on teleparallel Killing vector fields in Bianchi type VIII and IX space–times in teleparallel theory of gravitation Ghulam Shabbir, Amjad Ali, and Suhail Khan. Chin. Phys. B, 2011, 20(7): 070401.
[15]	Determining the long living quasi-normal modes of relativistic stars Lü Jun-Li(吕君丽) and Suen Wai-Mo(孙纬武) . Chin. Phys. B, 2011, 20(4): 040401.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Cite this article:

Online attention