Abstract
In the present article, Lie group symmetries of the master equation describing the shear free non-static fluid spheres with heat flow (Msomi et al. in Gen. Relativ. Gravit. 43(6):1685–1696, 2011) are exploited to yield wider class of solutions. Further the master equation is transformed in to more convenient modified form, which is capable of yielding numerous solutions rather easily. Moreover two non-point transformations are suggested under which the master equation and its modified form are invariant, which are utilised to generate new solutions starting with the known seed solutions.
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Msomi, A.M., Govinder, K.S., Maharaj, S.D.: New shear-free relativistic models with heat flow. Gen. Relativ. Gravit. 43(6), 1685–1696 (2011)
Deng, Y.: Solutions of the Einstein equations with heat flow. Gen. Relativ. Gravit. 21(5), 503–507 (1989)
Maiti, S.R.: Fluid with heat flux in a conformally flat space-time. Phys. Rev. D 25(10), 2518–2520 (1982)
Bergmann, O.: A cosmological solution of the Einstein equations with heat flow. Phys. Lett. A 82(8), 383 (1981)
Modak J, B.: Cosmological solution with an energy flux. J. Astrophys. Astron. 5, 317–322 (1984)
Krasinski, A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)
Triginer, J., Pavon, D.: Heat transport in an inhomogeneous spherically symmetric universe. Class. Quantum Gravity 12(3), 689–698 (1995)
Deng, Y., Mannheim, P.D.: Shear-free spherically symmetric inhomogeneous cosmological model with heat flow and bulk viscosity. Phys. Rev. D 42(2), 371–383 (1990)
Chang, Z., Guan, C.B., Huang, C.G., Lin, X.: Gravitational collapse of a spherical star with heat flow as a possible energy mechanism of gamma-ray bursts. Commun. Theor. Phys. 50(1), 271 (2008)
Santos, N.O.: Non-adiabatic radiating collapse. Mon. Not. R. Astron. Soc. 216, 403–410 (1985)
Banerjee, A., Dutta, S.B., Bhui, B.K.: Spherically symmetric solutions with heat flow in general relativity. Parmana J. Phys. 34(5), 397–401 (1990)
Glass, E.N.: A spherical collapse solution with neutrino outflow. J. Math. Phys. 31(8), 1974–1977 (1990)
Kustaanheimo, P., Qvist, B.: A note on some general solutions of the Einstein field equations in a spherically symmetric world. Comment. Phys. Math. Helsingf. 13, 1 (1948)
Kumar, S., Gupta, Y.K., Sharma, J.R.: Some static and non-static cylindrical symmetric perfect fluid distributions in general relativity. Int. Trans. Appl. Sci. 1, 527 (2009)
Bluman, G.W., Kumei, S.K.: Symmetries and Differential Equations. Springer, New York (1989)
Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, New York (1986)
Buchdahal, H.A.: Reciprocal static solutions of the equations of the gravitational field. Aust. J. Phys. 9, 116 (1956)
Vaidya, P.C.: Newtonian’ time in general relativity. Nature 171, 260–261 (1953)
Nariai, H.: On some static solutions of Einstein’s gravitational field equations in a spherically symmetric case. Sci. Rep. Tôhoku Univ. Ser., I. 34, 160–167 (1950)
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Maurya, S.K., Gupta, Y.K. Some New Solutions for Shear-Free Fluid Spheres with Heat Flow. Int J Theor Phys 52, 1075–1087 (2013). https://doi.org/10.1007/s10773-012-1422-1
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DOI: https://doi.org/10.1007/s10773-012-1422-1