Please wait a minute...
Chin. Phys., 2006, Vol. 15(1): 66-76    DOI: 10.1088/1009-1963/15/1/011
GENERAL Prev   Next  

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

Gao Ya-Jun
Department of Physics, Bohai University, Jinzhou 121000,China
Abstract  The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with $p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group $\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Keywords:  extended hyperbolic complex function method      general relativity      symmetry group  
Received:  16 May 2005      Revised:  04 July 2005      Published:  20 January 2006
PACS:  02.20.-a (Group theory)  
  02.10.Ud (Linear algebra)  
Fund: Project supported by the Science Foundation from Education Department of Liaoning Province, China (Grant No 202142036) and the National Natural Science Foundation of China (Grant No 10475036).

Cite this article: 

Gao Ya-Jun New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields 2006 Chin. Phys. 15 66

[1] 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.
[2] The mass limit of white dwarfs with strong magnetic fields in general relativity
Wen De-Hua, Liu He-Lei, Zhang Xiang-Dong. Chin. Phys. B, 2014, 23(8): 089501.
[3] Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity
Gamal G. L. Nashed. Chin. Phys. B, 2013, 22(2): 020401.
[4] Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity
Gamal G. L. Nashed. Chin. Phys. B, 2012, 21(6): 060401.
[5] 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.
[6] Finite symmetry transformation group of the Konopelchenko–Dubrovsky equation from its Lax pair
Hu Han-Wei,Yu Jun. Chin. Phys. B, 2012, 21(2): 020202.
[7] Symmetry groups and Gauss kernels of Schrödinger equations
Kang Jing,Qu Chang-Zheng. Chin. Phys. B, 2012, 21(2): 020301.
[8] Cosmological application on five-dimensional teleparallel theory equivalent to general relativity
Gamal G. L. Nashed. Chin. Phys. B, 2012, 21(10): 100401.
[9] Five-dimensional teleparallel theory equivalent to general relativity, the axially symmetric solution, energy and spatial momentum
Gamal G.L. Nashed. Chin. Phys. B, 2011, 20(11): 110402.
[10] Symmetry analysis and explicit solutions of the (3+1)-dimensional baroclinic potential vorticity equation
Hu Xiao-Rui, Chen Yong, Huang Fei. Chin. Phys. B, 2010, 19(8): 080203.
[11] Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic potential vorticity equation
Zhang Huan-Ping, Li Biao, Chen Yong, Huang Fei. Chin. Phys. B, 2010, 19(2): 020201.
[12] Gravitational radiation fields in teleparallel equivalent of general relativity and their energies
Gamal G.L. Nashed. Chin. Phys. B, 2010, 19(11): 110402.
[13] Neutrino oscillation interference phase in Kerr space--time
Ren Jun, Jia Meng-Wen, Yuan Chang-Qing. Chin. Phys. B, 2009, 18(12): 5575-5582.
[14] Orbital effect in the stationary axisymmetric field
Gong Tian-Xi, Wang Yong-Jiu. Chin. Phys. B, 2008, 17(7): 2356-2360.
[15] The classification of travelling wave solutions and superposition of multi-solutions to Camassa-- Holm equation with dispersion
Liu Cheng-Shi. Chin. Phys. B, 2007, 16(7): 1832-1837.
No Suggested Reading articles found!