Abstract
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.
Similar content being viewed by others
References
M S R Delgaty and K Lake,Comput. Phys. Commun. 115, 395 (1998)
M R Finch and J F E Skea, Preprint available on the web: http://edradour.symbcomp.uerj.br/pubs.html (1998)
H Stephani, D Kramer, M A H MacCullum, C Hoenslaers and E Herlt,Exact solutions of Einstein’s field equations (Cambridge University Press, Cambridge, 2003)
K Dev and M Gleiser,Gen. Relativ. Gravit. 34, 1793 (2002)
K Dev and M Gleiser,Gen. Relativ. Gravit. 35, 1435 (2003)
L Herrera, J Martin and J Ospino,J. Math. Phys. 43, 4889 (2002)
L Herrera, A D Prisco, J Martin, J Ospino, N O Santos and O Troconis,Phys. Rev. D69, 084026 (2004)
B V Ivanov,Phys. Rev. D65, 10411 (2002)
M K Mak and T Harko,Chinese J. Astron. Astrophys. 2, 248 (2002)
M Mak and T Harko,Proc. R. Soc. London A459, 393 (2003)
R Sharma and S Mukherjee,Mod. Phys. Lett. A17, 2535 (2002)
S Rahman and M Visser,Class. Quantum Gravit. 19, 935 (2002)
K Lake,Phys. Rev. D67, 104015 (2003)
D Martin and M Visser,Phys. Rev. D69, 104028 (2004)
P Boonserm, M Visser and S Weinfurtner, arXiv:gr-qc/0503007 (2005)
S D Maharaj and M Chaisi,Math. Meth. Appl. Sci. 29, 67 (2006)
S D Maharaj and R Maartens,Gen. Relativ. Gravit. 21, 899 (1989)
M K Gokhroo and A L Mehra,Gen. Relativ. Gravit. 26, 75 (1994)
M Chaisi and S D Maharaj,Gen. Relativ. Gravit. 37, 1177 (2005)
M Chaisi and S D Maharaj,Pramana-J. Phys. to appear (2006)
W C Saslaw, S D Maharaj and N Dadhich,Astrophys. J. 471, 571 (1996)
W C Saslaw,Gravitational physics of stellar and galactic systems (Cambridge University Press, Cambridge, 2003)
S Wolfram,Mathematica (Wolfram, Redwood City, 2003)
S D Maharaj and P G L Leach,J. Math. Phys. 37, 430 (1996)
C E Rhoades and R Ruffini,Phys. Rev. Lett. 32, 324 (1974)
R L Bowers and E P T Liang,Astrophys. J. 188, 657 (1974)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chaisi, M., Maharaj, S.D. A new algorithm for anisotropic solutions. Pramana - J Phys 66, 313–324 (2006). https://doi.org/10.1007/BF02704387
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02704387