The stability of a shearing viscous star with an electromagnetic field

doi:10.1088/1674-1056/22/5/050401

Abstract We analyze the role of the electromagnetic field for the stability of a shearing viscous star with spherical symmetry. Matching conditions are given for the interior and the exterior metrics. We use a perturbation scheme to construct the collapse equation. The range of instability is explored in Newtonian and post Newtonian (pN) limits. We conclude that the electromagnetic field diminishes the effects of the shearing viscosity in the instability range and makes the system more unstable in both Newtonian and post Newtonian approximations.

Keywords: gravitational collapse electromagnetic field instability

Received: 24 September 2012
Revised: 06 November 2012
Accepted manuscript online:

PACS:	04.20.-q	(Classical general relativity)
	04.25.Nx	(Post-Newtonian approximation; perturbation theory; related Approximations)
	04.40.Dg	(Relativistic stars: structure, stability, and oscillations)
	04.40.Nr	(Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields)

Corresponding Authors: M. Sharif, M. Azama
E-mail: msharif.math@pu.edu.pk; azammath@gmail.com

Cite this article:

M. Sharif, M. Azama The stability of a shearing viscous star with an electromagnetic field 2013 Chin. Phys. B 22 050401

[1]	Sharif M and Abbas G 2010 Astrophys. Space Sci. 327 285
[2]	Sharif M and Abbas G 2011 J. Phys. Soc. Jpn. 80 104002
[3]	Sharif M and Abbas G 2013 Chin. Phys. B 22 030401
[4]	Eddington A S 1926 Internal Constitution of the Stars (Cambrigde: Cambrigde University Press)
[5]	Glendenning N 2000 Compact Stars (Berlin: Springer)
[6]	Rosseland S 1924 Mon. Not. R. Astron. Soc. 84 720
[7]	de la Cruz V and Israel W 1967 Nuovo Cimento A 51 744
[8]	Bekenstein J 1970 Phys. Rev. D 4 2185
[9]	Olson E and Bailyn M 1976 Phys. Rev. D 13 2204
[10]	Mashhoon B and Partovi M 1979 Phys. Rev. D 20 2455
[11]	Zhang J L, Chau W Y and Deng T Y 1982 Astrophys. Space Sci. 88 81
[12]	Ghezzi C 2005 Phys. Rev. D 72 104017
[13]	Barreto W, Rodrguez B, Rosales L and Serrano O 2007 Gen. Relativ. Gravit. 39 537
[14]	Chandrasekhar S 1964 Astrophys. J. 140 417
[15]	Herrera L, Santos N O and Le Denmat G 1989 Mon. Not. R. Astron. Soc. 237 257
[16]	Chan R, Kichenassamy S, Le Denmat G and Santos N O 1989 Mon. Not. R. Astron. Soc. 239 91
[17]	Chan R, Herrera L and Santos N O 1993 Mon. Not. R. Astron. Soc. 265 533
[18]	Chan R, Herrera L and Santos N O 1994 Mon. Not. R. Astron. Soc. 267 637
[19]	Herrera L, Santos N O and Le Denmat G 2012 Gen. Relativ. Gravit. 44 1143
[20]	Chan R 2000 Mon. Not. R. Astron. Soc. 316 588
[21]	Horvat D, Ilijic S and Marunovic A 2011 Class. Quantum Grav. 28 25009
[22]	Hernandez H, Nunez L A and Percoco U 1999 Class. Quantum Grav. 16 871
[23]	Hernandez H and Nunez L A 2004 Can. J. Phys. 82 29
[24]	Sharif M and Kausar H R 2012 Astrophys. Space Sci. 337 805
[25]	De Felice F, Yu Y and Fang Z 1995 Mon. Not. R. Astron. Soc. 277 L17
[26]	De Felice F, Siming L and Yunqiang Y 1999 Class. Quantum Grav. 16 2669
[27]	De Felice F, Siming L and Yunqiang Y 2003 Phys. Rev. D 68 084004
[28]	Stettner R 1973 Ann. Phys. 80 212
[29]	Glazer I 1976 Ann. Phys. 101 594
[30]	Mak M, Dobson P and Harko T 2001 Europhys. Lett. 55 310
[31]	Misner C W and Sharp D 1964 Phys. Rev. 136 B571
[32]	Giuliani A and Rothman T 2008 Gen. Relativ. Gravit. 40 1427
[33]	Andreasson H 2009 Commun. Math. Phys. 288 715
[34]	Bohmer C and Harko T 2007 Gen. Relativ. Gravit. 39 757
[35]	Buchdahl H 1959 Phys. Rev. 116 1027
[36]	Sharif M and Azam M 2012 JCAP 02 043
[37]	Darmois G 1927 Memorial des Sciences Mathematiques (Gautheir-Villars)
[38]	Harrison B K, Thorne K S, Wakano M and Wheeler J A 1965 Gravitation Theory and Garvitational Collapse (Chicago: University of Chicago Press)
[39]	Pinheiro G and Chan R 2012 Gen. Relativ. Gravit. 45 213
[40]	Ernesto F E and Simeone C 2011 Phys. Rev. D 83 104009

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