Astrophysics and Space Science

, Volume 355, Issue 1, pp 171–177 | Cite as

Modeling quasar central engine as a relativistic radiating star

Original Article


Long ago Hoyle & Fowler attempted to model the central engine of quasars as hot super-massive stars supported by radiation pressure. Whereas the model of Hoyle & Fowler was Newtonian, here we make a toy model of quasar central engines as ultra relativistic ultrahot plasma or as a ball of radiation. Accordingly, we consider general relativistic gravitational collapse including emission of radiation. More specifically, we discuss a new class of radiating fluid ball exact solution in conformally-flat metric which is quasi-static and contracting at negligible rate. The problem is solved by assuming that the metric potential is separable in to radial and time dependent parts. It is found the gravitational mass of the radiating ball M→0 as comoving time t→∞ in conformity of the idea of an “Eternally Collapsing Object” (ECO) which has been claimed to be the true nature of the so-called “Black Holes”. In particular, we consider here a quasi-static radiation ball having M≈9.507×107M, a radius of ≈2×1014 km, and a luminosity L≈9.1×1046 erg/s. Prima-facie, such an ECO solution is compatible with the central compact object of a quasar having comoving lifetime of ≈107 yr and a distantly observed lifetime (u) which could be higher by many orders of magnitude.


Gravitational collapse Quasar Vaidya metric Conformally-flat metric 



Authors are grateful to the anonymous referee for his rigorous review, constructive comments and useful suggestions.


  1. Bonnor, W.B., de Oliveira, A.K.G., Santos, N.O.: Phys. Rep. 181, 269 (1989)ADSMathSciNetCrossRefGoogle Scholar
  2. de Oliveira, A.K.G., Santos, N.O.: Astrophys. J. 312, 640 (1987)ADSCrossRefGoogle Scholar
  3. de Oliveira, A.K.G., Kolassis, C.A., Santos, N.O.: Mon. Not. R. Astron. Soc. 231, 1011 (1988)ADSCrossRefGoogle Scholar
  4. de Oliveira, A.K.G., Santos, N.O., Kolassis, C.A.: Mon. Not. R. Astron. Soc. 216, 101 (1995)Google Scholar
  5. Debnath, U., Nath, S., Chakraborty, S.: Gen. Relativ. Gravit. 37, 215 (2005)ADSCrossRefGoogle Scholar
  6. Fowler, W.A.: Astrophys. J. 144, 180 (1966)ADSCrossRefGoogle Scholar
  7. Glass, E.N.: Phys. Lett. A 86, 351 (1981)ADSCrossRefGoogle Scholar
  8. Herrera, L., Jimenez, J., Ruggeri, G.L.: Phys. Rev. D 22, 2305 (1980)ADSMathSciNetCrossRefGoogle Scholar
  9. Herrera, L., Di Prisco, A., Hernandez Pastora, A., Santos, N.O.: Phys. Lett. A 237, 113 (1998)ADSCrossRefGoogle Scholar
  10. Herrera, L., LeDenmat, G., Santos, N.O., Wang, A.: Int. J. Mod. Phys. D 13, 583 (2004a)ADSCrossRefGoogle Scholar
  11. Herrera, L., Di Prisco, A., Martin, J., Ospino, J., Santos, N.O., Triconis, U.: Phys. Rev. D 69, 084026 (2004b)ADSCrossRefGoogle Scholar
  12. Herrera, L., Di Prisco, A., Ospino, J.: Phys. Rev. D 74, 044001 (2006)ADSCrossRefGoogle Scholar
  13. Herrera, L., Ospino, J., Di Prisco, A., Fuenmayor, E., Troconis, O.: Phys. Rev. D 79, 064025 (2009)ADSMathSciNetCrossRefGoogle Scholar
  14. Hoyle, F., Fowler, W.A.: Mon. Not. R. Astron. Soc. 125, 16 (1963)Google Scholar
  15. Kramer, D.: J. Math. Phys. 33, 1458 (1992)ADSMathSciNetCrossRefGoogle Scholar
  16. Lindquist, R.W., Schwarz, R.A., Misner, C.W.: Phys. Rev. B 137, 1364 (1965)ADSCrossRefGoogle Scholar
  17. Maharaj, S.D., Govender, M.: Aust. J. Phys. 50, 959 (1997)ADSGoogle Scholar
  18. Maharaj, S.D., Govender, M.: Int. J. Mod. Phys. D 14, 667 (2005)ADSCrossRefGoogle Scholar
  19. Misner, C.W.: Phys. Rev. B 137, 1350 (1965)MathSciNetCrossRefGoogle Scholar
  20. Mitra, A.: (1998). eprint arXiv:astro-ph/9811402
  21. Mitra, A.: New Astron. 12, 146 (2006a)ADSCrossRefGoogle Scholar
  22. Mitra, A.: Phys. Rev. D 74, 024010 (2006b)ADSCrossRefGoogle Scholar
  23. Mitra, A.: Mon. Not. R. Astron. Soc. Lett. 367, L66 (2006c)ADSCrossRefGoogle Scholar
  24. Mitra, A.: Mon. Not. R. Astron. Soc. 369, 492 (2006d)ADSCrossRefGoogle Scholar
  25. Mitra, A.: Adv. Space Res. 38, 2917 (2006e)ADSCrossRefGoogle Scholar
  26. Mitra, A.: J. Math. Phys. 50, 042502 (2009a)ADSMathSciNetCrossRefGoogle Scholar
  27. Mitra, A.: Pramana 73, 615 (2009b). arXiv:0911.3518 ADSCrossRefGoogle Scholar
  28. Mitra, A.: Astrophys. Space Sci. 332, 43 (2011a)ADSCrossRefGoogle Scholar
  29. Mitra, A.: J. Cosmol. 17, 7376 (2011b)ADSGoogle Scholar
  30. Mitra, A.: Int. J. Astron. Astrophys. 2(4), 236 (2012)CrossRefGoogle Scholar
  31. Mitra, A.: Int. J. Mod. Phys. D 22, 1350021 (2013)ADSCrossRefGoogle Scholar
  32. Mitra, A., Glendenning, N.K.: Mon. Not. R. Astron. Soc. Lett. 404, L50 (2010)ADSCrossRefGoogle Scholar
  33. Mitra, A., Krori, K.D.: J. Cosmol. 17, 7064 (2011)Google Scholar
  34. Mitra, A., Singh, K.K.: Int. J. Mod. Phys. D 22, 1350054 (2013)ADSCrossRefGoogle Scholar
  35. Naidu, N.F., Govinder, M.: J. Astrophys. Astron. 28, 167 (2007)ADSCrossRefGoogle Scholar
  36. Pant, D.N., Tewari, B.C.: Astrophys. Space Sci. 163, 223 (1989)ADSCrossRefGoogle Scholar
  37. Pant, D.N., Tewari, B.C.: Astrophys. Space Sci. 163, 273 (1990)CrossRefGoogle Scholar
  38. Pant, N., Tiwari, B.C.: Astrophys. Space Sci. 331, 645 (2010)ADSCrossRefGoogle Scholar
  39. Pant, N., et al.: Astrophys. Space Sci. 327, 279 (2011)ADSCrossRefGoogle Scholar
  40. Santos, N.O.: Mon. Not. R. Astron. Soc. 216, 403 (1985)ADSCrossRefGoogle Scholar
  41. Schild, R., Leiter, D., Robertson, S.L.: Astron. J. 132, 420 (2006)ADSCrossRefGoogle Scholar
  42. Tewari, B.C.: Astrophys. Space Sci. 149, 233 (1988)ADSMathSciNetCrossRefGoogle Scholar
  43. Tewari, B.C.: Indian J. Pure Appl. Phys. 32, 504 (1994)Google Scholar
  44. Tewari, B.C.: Astrophys. Space Sci. 306, 273 (2006)ADSCrossRefGoogle Scholar
  45. Vaidya, P.C.: Phys. Rev. 83, 10 (1951)ADSCrossRefGoogle Scholar
  46. Vaidya, P.C.: Nature 171, 260 (1953)ADSMathSciNetCrossRefGoogle Scholar
  47. Vaidya, P.C.: Astrophys. J. 144, 343 (1966)ADSCrossRefGoogle Scholar
  48. Weinberg, S.: Gravitation and Cosmology. Wiley, NY (1972)Google Scholar
  49. Zeldovich, Ya.B.: Sov. Phys. JETP 14, 1143 (1962)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhysicsNational Defense AcademyPuneIndia
  2. 2.Department of MathematicsNational Defence AcademyPuneIndia

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