Abstract
A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. The formulas for the characteristics of the model are straight and tractable. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time-dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Herrera L., Di Prisco A., Ospino J.: Phys. Rev. D 74, 044001 (2006)
Santos N.O.: Mon. Not. R. Astron. Soc. 216, 403 (1985)
Krasinski A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)
Bonnor W.B., De Oliveira A.K.G., Santos N.O.: Phys. Rep. 5, 269 (1989)
Kustanheimo P., Qvist B.: Comm. Phys. Math. Helsingf. 13, 16 (1948)
Glass E.N.: J. Math. Phys. 20, 1508 (1979)
Stephani H., Kramer D., Maccalum M., Hoenselaers C., Herlt E.: Exact Solutions to Einstein’s Field Equations. Cambridge University Press, Cambridge (2003)
Ivanov B.V.: Int. J. Mod. Phys. A 25, 3975 (2010)
Ivanov B.V.: Int. J. Mod. Phys. D 20, 319 (2011)
Msomi A.M., Govinder K.S., Maharaj S.D.: Gen. Relativ. Gravit. 43, 1685 (2011)
Msomi A.M., Govinder K.S., Maharaj S.D.: Int. J. Theor. Phys. 51, 1290 (2012)
Kuchowicz B.: Phys. Lett. A 35, 223 (1971)
Kuchowicz B.: Acta Phys. Pol. B 3, 209 (1972)
Goldman S.P.: Astrophys. J. 226, 1079 (1978)
Stewart B.V.: J. Phys. A 15, 1799 (1982)
Knutsen H.: Gen. Relativ. Gravit. 23, 843 (1991)
Rahman S., Visser M.: Class. Quantum Grav. 19, 935 (2002)
Lake K.: Phys. Rev. D 67, 104015 (2003)
Herrera L., Le Denmat G., Santos N.O., Wang A.: Int. J. Mod. Phys. D 13, 583 (2004)
Maharaj S.D., Govender M.: Int. J. Mod. Phys. D 14, 667 (2005)
Mishtry S.S., Maharaj S.D., Leach P.G.L.: Math. Meth. Appl. Sci. 31, 363 (2008)
De Oliveira A.K.G., Santos N.O., Kolassis C.A.: Mon. Not. R. Astron. Soc. 216, 1001 (1985)
De Oliveira A.K.G., De Pacheco J.A.F., Santos N.O.: Mon. Not. R. Astron. Soc. 220, 405 (1986)
De Oliveira A.K.G., Kolassis C.A., Santos N.O.: Mon. Not. R. Astron. Soc. 231, 1011 (1988)
Banerjee A., Chatterjee S., Dadhich N.: Mod. Phys. Lett. A 17, 2335 (2002)
Herrera L., Ospino J., Di Prisco A., Fuenmayor E., Troconis O.: Phys. Rev. D 79, 064025 (2009)
Govender M., Maharaj S.D., Maartens R.: Class. Quantum Grav. 15, 323 (1998)
Govender M., Maartens R., Maharaj S.D.: Mon. Not. R. Astron. Soc. 310, 557 (1999)
Govinder K.S., Govender M.: Phys. Lett. A 283, 71 (2001)
Pinheiro G., Chan R.: Gen. Relativ. Gravit. 40, 2149 (2008)
Joshi P.S., Malafarina D., Narayan R.: Class. Quantum Grav. 28, 235018 (2011)
Kuchowicz B.: Acta Phys. Pol. B 4, 415 (1973)
Buchdahl H.A.: Aust. J. Phys. 9, 13 (1956)
Glass E.N.: Phys. Lett. A 86, 351 (1981)
Banerjee A., Chatterjee S.: Astrophys. Space Sci. 299, 219 (2005)
Govinder K.S., Govender M.: Gen. Relativ. Gravit. 44, 147 (2012)
Banerjee A., Dutta Choudhury S.B., Bhui B.K.: Phys. Rev. D 40, 670 (1989)
Gürses M., Gürsey Y.: Nuovo Cim. B 25, 786 (1975)
Kramer D.: J. Math. Phys. 33, 1458 (1992)
Maharaj S.D., Govender M.: Aust. J. Phys. 50, 959 (1997)
Strobel H.: Jena. Math. Naturw. Reihe 17, 195 (1968)
Maiti S.R.: Phys. Rev. D 25, 2518 (1982)
Sanyal A.K., Ray D.: J. Math. Phys. 25, 1975 (1984)
Modak B.: J. Astrophys. Astr. 5, 317 (1984)
Deng Y.: Gen. Relativ. Gravit. 21, 503 (1989)
Deng Y., Mannheim P.D.: Phys. Rev. D 42, 371 (1990)
Som M.M., Santos N.O.: Phys. Lett. A 87, 89 (1981)
Thirukkanesh S., Maharaj S.D.: J. Math. Phys. 50, 022502 (2009)
Kolassis C.A., Santos N.O., Tsoubelis D.: Astrophys. J. 327, 755 (1988)
Chan R., Lemos J., Santos N.O., De Pacheco J.A.F.: Astrophys. J. 342, 976 (1989)
Grammenos T.: Astrophys. Space Sci. 211, 31 (1994)
Bergmann O.: Phys. Lett. A 82, 383 (1981)
Jiang S.: J. Math. Phys. 33, 3503 (1992)
Nariai H.: Prog. Theor. Phys. 38, 92 (1967)
Buchdahl H.A.: Astrophys. J. 140, 1512 (1964)
Bayin S.: Phys. Rev. D 18, 2745 (1978)
Narlikar V.V., Patwardhan G.K., Vaidya P.C.: Proc. Nat. Inst. Sci. India 9, 229 (1943)
Nariai H.: Sci. Rep. Tohoku Univ. 34, 160 (1950)
Kuchowicz B.: Indian J. Pure Appl. Math. 2, 297 (1971)
Pant D.N., Sah A.: Phys. Rev. D 32, 1358 (1985)
Banerjee A., Dutta Choudhury S.B., Bhui B.K.: Pramana 34, 397 (1990)
Burlankov D.E.: Theor. Math. Phys. 95, 455 (1993)
Pant N., Mehta R.N., Pant M.J.: Astrophys. Space Sci. 330, 353 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ivanov, B.V. Collapsing shear-free perfect fluid spheres with heat flow. Gen Relativ Gravit 44, 1835–1855 (2012). https://doi.org/10.1007/s10714-012-1370-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-012-1370-3