Abstract
A family of static solutions of the Einstein field equations with spherical symmetry for a locally anisotropic fluid with homogeneous energy density is obtained. These solutions depend on two adjustable parameters related to degree of anisotropy of the fluid. Some known solutions may be recovered for specific values of these parameters. As a difference to other known solutions it is possible to change the grade of anisotropy of the model, keeping the same functional dependence on the coordinates. By means of a slow adiabatic contraction, the stability of the obtained solutions is studied. Also, it is shown, how it is possible to enhance the stability of the models by adjusting the parameters, and to obtain more compact configurations than those obtained with other similar anisotropic solutions, while the dominant or strong energy condition holds within the sphere.
Similar content being viewed by others
References
Lemaitre G. (1933). Ann. Soc. Sci. Bruxelles A 53: 51
Florides P.S. (1974). Proc. R. Soc. Lond. A 337: 529
Bowers R.L. and Liang E.P.T. (1974). Anisotropic spheres in general relativity. Astrophys. J. 188: 657–665
Letelier P. (1980). Phys. Rey. D 22: 807
Cosenza M., Herrera L., Esculpi M. and Witten L. (1981). J. Math. Phys. 22: 118
Bayin S. (1982). Phys. Rey. D 26: 1262
Krori K.D., Borgohain P., Can R. and Devi (1984). J. Phys. 62: 239
Bondi H. (1992). Mon. Not. R. Astron. Soc. 259: 365
Ponce de Leon J. (1987). J. Math. Phys. 28: 1114
Herrera L. (1992). Phys. Lett. A 165: 206
Herrera L. and Santos N.O. (1997). Phys. Rep. 286: 53
Gokhroo M. and Mehra A. (1994). Gen. Rel. Grav. 26: 75
Mak M., Dobson P. and Harko T. (2002). Int. J. Mod. Phys. D 11: 207
Chaisi M. and Maharaj D. (2005). Gen. Rel. Grav. 37: 1177
Mak M. and Harko T. (2003). Proc. Roy. Soc. Lond. A 459: 393
Ruderman R. (1972). Ann. ihv. Astron. Astrophys. 10: 427
Sokolov, A.1.: JETP 7, 1337 (1980)
Canuto V. (1974). Annu. Rev. Astron. Astrophys. 12: 167
Glendenning, N.K.: Compact stars: nuclear physics, particle physics and general relativity. In: Heiselberg, H., Jensen, M.-H. (eds.) Phys. Rep. 328, 237 (2000).
Heinztmann, H., Hillebrandt, W.: Astron. Astrophys. 38, 51–55
Sawyer R.F. (1972). Phys. Rey. Lett. 29: 382
Cattoen C., Faber T. and Visser M. (2005). Class. Quantum Grav. 22: 4189
Mazur, P.O., Mottola, E.: Gravitational condensate stars: an altemative to black roles [arXiv:gr-qc/0109035]
Bondi H. (1999). Mon. Not. R. Astron. Soc. 302: 337
Ivanov B.V. (2002). Phys. Rev. D 65: 104011
Barraco D., Hamity V. and Gleiser R. (2003). Phys. Rev. D 67: 064003
Dev K. Gleiser M. (2002). Gen. Rel. Grav. 34: 1793
Herrera L., Ruggeri G. and Witten L. (1979). Astrophys. J. 234: 1094
Bondi H. (1964). Proc. R. Soc. A 281: 39
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Esculpi, M., Malaver, M. & Aloma, E. A comparative analysis of the adiabatic stability of anisotropic spherically symmetric solutions in general relativity. Gen Relativ Gravit 39, 633–652 (2007). https://doi.org/10.1007/s10714-007-0409-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-007-0409-3