SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME

doi:10.1016/S0252-9602(14)60059-X

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 917-931.doi: 10.1016/S0252-9602(14)60059-X

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SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME

LUO Shao-Sheng*, LIU Qi

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received:2013-05-21 Revised:2013-09-01 Online:2014-05-20 Published:2014-05-20
About author:LUO Shao-Sheng|11206010@zju.edu.cn
Supported by:
This work was in part supported by the NNSF of China (11271323).

Abstract

Abstract:

In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordstr¨om space-time. The equation of relativistic membranes moving in the Reissner-Nordstr¨om space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstr¨om space-time.

Key words: Reissner-Nordstr¨om space-time, nonlinear wave equation, spherical symmetric solution, null-membrane, horizon

CLC Number:

35L70

LUO Shao-Ying, LIU Qi. SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME[J].Acta mathematica scientia,Series B, 2014, 34(3): 917-931.

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References

[1] Allen P, Andersson L, Isenberg,J. Timelike minimal submanifolds of general co-dimension in Minkowski space time. J Hyperbolic Differ Equ, 2006, 3(4): 691–700

[2] Brendle S. Hypersurfaces in Minkowski space with vanishing mean curvature. Comm Pure Appl Math, 2002, 55(10): 1249–1279

[3] Gu Chaohao. A global study of extremal surfaces in 3-dimensional Minkowski space//Gu Chaohao, Berger M, Bryant R L. Differential geometry and differential equations. Berlin: Springer-Verlag, 1987: 26–33

[4] Gu Chaohao. A class of boundary problems for extremal surfaces of mixed type in Minkowski 3-space. J Reine Angew Math, 1988, 385: 195–202

[5] Lindblad H. A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time. Proc Amer Math Soc, 2004, 132(4): 1095–1102

[6] Bordeman M, Hoppe J. The dynamics of relativistic membranes: Reduction to 2-dimensional fluid dynam-ics. Phys Lett B, 1993, 317(3): 315–320

[7] Huang Shoujun, Kong Dexing. Equations for the motion of relativistic torus in the Minkowski space R¹⁺ⁿ. J Math Phys, 2007, 48(8): 083510

[8] DeVega H J, Sanches N. Lectures on String Theory in Curved Spacetimes[M]//String Gravity and Physics at the Planck Energy Scale. Netherlands: Springer, 1996: 11–63

[9] Roshchupkin S N, Zheltukhin A A. On a Possibility of Membrane Cosmology (Preprint)

[10] Lax P D. Hyperbolic systems of conservation laws II. Commun. Pure Appl Math, 1957, 10(4): 537–556

[11] Majda A. Compressible Fluid Flow and System of Conservation Laws in Several Space Variables. Applied Mathematical Sciences 53. New York: Springer-Verlag, 1984

[12] He Chunlei, Kong Dexing. Spherical symmetric solutions for the motion of relativistic membranes in the Schwarzschild spacetime. Journal of Mathematical Physics, 2009, 50(8): 083516

[13] Osserman R. A survey of minimal surfaces[M]. Second edition. New York: Dover Publications, Inc, 1986

[14] Lelyakov A, Roshchupkin S. Null Membranes in Dyonic Black Hole Background. Turkish Journal of Physics, 2003, 27: 293–298

[15] Bandos I A, Zheltukhin A A. Null Super P-Branes Quantum Theory in 4-Dimensional Space-Time. Fortschr Phys, 1993, 41(7): 619–676

[16] Kar S. Schild´s null strings in flat and curved backgrounds. Physical Review D, 1996, 53(12): 6842–6846

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME

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