Abstract
In this paper we present a general framework for generating exact solutions to the Einstein field equations for static, anisotropic fluid spheres in comoving, isotropic coordinates obeying a linear equation of state of the form \(p_{r} =\alpha \rho - \beta\). We show that all possible solutions can be obtained via a single generating function defined in terms of one of the gravitational potentials. The physical viability of our solution-generating method is illustrated by modeling a static fluid sphere describing a strange star.
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Bonnor, W.B., de Oliveira, A.K.G., Santos, N.O.: Phys. Rep. 181, 269 (1989)
Bowers, R.L., Liang, E.P.T.: Astrophys. J. 188, 657 (1974)
Buchdahl, H.A.: Phys. Rev. 116, 1027 (1959)
de Sitter, W.: Proc. R. Acad. Amst. 19, 1217 (1917)
Dev, K., Gleiser, M.: Gen. Relativ. Gravit. 34, 1793 (2002)
Dev, K., Gleiser, M.: Gen. Relativ. Gravit. 35, 1435 (2003)
Dey, M., Bombaci, I., Dey, J., Ray, S., Samantha, B.C.: Phys. Lett. B 438, 123 (1998)
Einstein, A.: Sitz. Deut. Akad. Wiss. Math.-Phys. Berlin 8, 142 (1917)
Esculpi, M., Malaver, M., Aloma, E.: Gen. Relativ. Gravit. 39, 633 (2007)
Finch, M.R., Skea, J.E.F.: http://edradour.symbcomp.uerj.br/pubs.html (1995)
Herrera, L., Barreto, W.: Phys. Rev. D 88, 084022 (2013)
Herrera, L., Santos, N.O.: Phys. Rep. 286, 53 (1997)
Herrera, L., Le Denmat, G., Santos, N.O., Wang, A.: Int. J. Mod. Phys. D 13, 583 (2004)
Herrera, L., di Prisco, A., Ospino, J.: Phys. Rev. D 74, 044001 (2006)
Herrera, L., Ospino, J., Di Prisco, A.: Phys. Rev. D 77, 027502 (2008)
Herrera, L., Di Prisco, A., Ibanez, J., Ospino, J.: Phys. Rev. D 87, 024014 (2013)
Ivanov, B.V.: Gen. Relativ. Gravit. 44, 1835 (2012)
Kramer, D.: J. Math. Phys. 33, 1458 (1992)
Kustaanheimo, P., Qvist, B.: Phys. Math. Helsingf. 13, 1 (1948)
Lake, K.: Phys. Rev. D 67, 104015 (2003)
Leahy, D.A.: Astrophys. J. 613, 517 (2004)
Maharaj, S.D., Govender, M.: Aust. J. Phys. 50, 959 (1997)
Maharaj, S.D., Govender, M.: Int. J. Mod. Phys. D 667, 14 (2005)
Maharaj, S.D., Takisa, P.M.: Gen. Relativ. Gravit. 44, 1419 (2012)
Mak, M.K., Harko, T.: Pramana J. Phys. 65, 185 (2005)
Muñoz-Darias, T., Casares, J., O’Brien, K., Steeghs, D., Martínez-Pais, I.G., Cornelisse, R., Charles, P.A.: Mon. Not. R. Astron. Soc. 394, L136–L140 (2009)
Ngubelanga, S.A., Maharaj, S.D.: Adv. Math. Phys. 2013, 905168 (2013)
Ngubelanga, S.A., Maharaj, S.D., Ray, S.: Astrophys. Space Sci. 357, 74 (2015a)
Ngubelanga, S.A., Maharaj, S.D., Ray, S.: Astrophys. Space Sci. 357, 40 (2015b)
Pant, N., Pradhan, N., Mohammad, H.M.: Astrophys. Space Sci. 352, 135 (2014a)
Pant, N., Pradhan, N., Mohammad, H.M.: Int. J. Theoret. Phys. 53, 3958 (2014b)
Pant, N., Pradhan, N., Malaver, M.: Int. J. Astrophys. Space Sci. 3, 1 (2015a)
Pant, N., Pradhan, N., Mohammad, H.M.: Astrophys. Space Sci. 355, 137 (2015b)
Rawls, M.L., Orosz, J.A., McClintock, J.E., Torros, M.A.P., Bailyn, C.D., Buxton, M.M.: Astrophys. J. 730, 25 (2011)
Schwarzschild, K.: Sitz. Deut. Akad. Wiss. Math.-Phys. Berlin 24, 424 (1916)
Sharma, R., Maharaj, S.D.: Mon. Not. R. Astron. Soc. 375, 1265 (2007)
Takisa, P.M., Maharaj, S.D., Subharthi, R.: Astrophys. Space Sci. 354, 2120 (2014)
Thirukkanesh, S., Ragel, F.C.: Astrophys. Space Sci. 354, 1883 (2014)
Thirukkanesh, S., Govender, M., Lortan, D.B.: IJMP-D 24, 1550002 (2015)
Tikekar, R., Jotania, K.: Pramana J. Phys. 68, 397 (2007)
Wyman, M.: Phys. Rev. D 70, 74 (1946)
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The authors are thankful to the anonymous referee for constructive suggestions which helped improve the main results of this paper.
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Govender, M., Thirukkanesh, S. Anisotropic static spheres with linear equation of state in isotropic coordinates. Astrophys Space Sci 358, 39 (2015). https://doi.org/10.1007/s10509-015-2431-3
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DOI: https://doi.org/10.1007/s10509-015-2431-3