Spherically symmetric model with electromagnetic field in stationary space-time (original) (raw)

Abstract

We have evaluated spherically symmetric model with electromagnetic field and with equation of state   p , where  is arbitrary constant, by solving Einstein's field equations in stationary space-time. It is observed that dust, radiating and stiff dominated spherically symmetric models does not exist. Spherically symmetric dark energy models exist and they are studied in regards with their geometrical and physical aspects in detail.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (46)

  1. Takeno H. On the Spherically Symmetric Space-Times in General Relativity, Progress of Theoretical Physics,1952:8(3):317-326.
  2. Karade TM. Spherically Symmetric Space-times in Bi-metric Relativity Theory -I, Indian J. Pure & Applied Mathematics,1980:11(9):1202-1209.
  3. Tikekar R. On spherically symmetric singularity-free models in relativistic cosmology, Pramana J. Phys.,2000:55(4):623-628.
  4. Abbassi AH, Gharanfoli S, Abbassi AM. General Spherically Symmetric Solutions of Einstein Vacuum Field Equations With Λ, Apeiron,2002,9(3).
  5. Borkar MS, Karade TM. On Singularity of Spherically Symmetric Space Times, Indian J. Pure & Applied Mathematics,2003:34(8):1219-1224.
  6. Sahoo PK. Spherically Symmetric Cosmological Models in Bimetric Theory, Bulg. J. Phys,2005:(32):175- 180.
  7. Sharif M, Yousaf Z. Shearfree Spherically Symmetric Fluid Models, Chin. Phys. Lett.,2012:29(5):50403.
  8. Parry AR. A Survey of Spherically Symmetric Spacetimes, 2012, arXiv: 1210.5269v1 [gr-qc].
  9. Maurya SK, Ratanpal BS, Govender M. Anisotropic stars for spherically symmetric spacetimes satisfying the Karmarkar condition, Annals of Phys.,2017:382:36-49.
  10. Pandya DN, Hasmani AH. Spherically Symmetric Charged Anisotropic Solution in Higher Dimensional Bimetric General Relativity, Int. J. Applications & Applied Mathematics,2020:15(1):58-68.
  11. Harrison ER. Origin of Magnetic Fields in the Early Universe, Phys. Rev. Lett.,1973:30(5):188-190.
  12. Melvin MA. Homogeneous Axial Cosmologies with Electromagnetic Fields and Dust, Ann. New York Acad. Sci.,1975:262:253-274.
  13. Upadhaya RD, Dave S. Some Magnetized Bianchi Type-III Massive String Cosmological Models in General Relativity, Brazilian J. Phys.,2008:38(4):615-620.
  14. Pradhan A, Singh SK, Yadav LS. String Cosmological Model in Cylindrically Symmetric Inhomogeneous Universe with Electromagnetic Field, Romanian Reports in Physics,2008:60(4):1013-1024.
  15. Pradhan A, Singh PK, Yadav AK. A Plane-Symmetric Inhomogeneous Cosmological Model of Perfect Fluid Distribution with Electromagnetic Field I, Commun. Theo. Phys.,2010:54(1):191-196.
  16. Tyagi A, Chhajed D. Homogeneous Anisotropic Bianchi Type IX Cosmological Model for Perfect Fluid Distribution with Electromagnetic Field, American J. Math. & Stat.,2012:2(3):19-21.
  17. Singh A, Upadhyay RC, Pradhan A. Some Bianchi Type-III Bulk Viscous Massive String Cosmological Models with Electromagnetic Field, ARPN J. Sci. & Tech.,2013:3(2):146-152.
  18. Bali R, Pradhan A, Rai A. String Cosmological Model in Cylindrically Symmetric Inhomogeneous Universe with Electromagnetic Field, Prespacetime J.,2014:5(7):695-705.
  19. Bhoyar SR, Chirde VR. Magnetized Anti-stiff fluid Cosmological Models with Variable Cosmological Constant, International Journal of Scientific Research in Mathematical and Statistical Sciences,2018:5(1):11-18.
  20. Charjan SS, Dhongle PR, Borkar MS. Bianchi Type I Bulk Viscous Fluid String Dust Magnetized Cosmological Model with Λ-Term in Bimetric Theory of Gravitation, International Journal of Scientific Research in Mathematical and Statistical Sciences,2019:6(3):35-40.
  21. Banerjee A, Sanyal AK. Homogeneous Anisotropic Cosmological Models with Viscous Fluid and Magnetic Field, 2021, arXiv: 2105.07235v1 [gr-qc].
  22. Perlmutter S. et al. Discovery of a Supernova Explosion at Half the Age of the Universe, Nature, 391, 1998, 51-54.
  23. Riess AG. et al. Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution, Astrophys. J., Vol. 607, 2004, pp. 665 -687.
  24. Trimble V., Existence and Nature of Dark Matter in the Universe, Annual Review of Astronomy and Astrophysics,1987:25:425-472.
  25. Peebles PJE, Ratra B. The Cosmological Constant and Dark Energy, Reviews of Modern Physics,2003:75(2):559-606.
  26. Chapline G. Dark Energy Stars, Proceedings of Texas Conference of Relativistic Astrophysics, Stanford, 2004.
  27. Lobo FSN. Stable Dark Energy Stars, Class. Quantum Gravit.,2007:23:1525-1541.
  28. Padmanabhan T. Dark Energy and Gravity, Gen. Relativ. Gravit.,2008:40:529-564.
  29. Chan R, da Silva MFA, da Rocha JFV. Star Models with Dark Energy, Gen. Relativ. Gravit.,2009:41:1835- 1851.
  30. Ghezzi CR. Anisotropic Dark Energy Stars, Astrophys. Space Sci.,2011:333:437-447.
  31. Rahaman F, et al. Singularity -Free Dark Energy Star, Gen. Relativ. Gravit.,2012:44:107-124.
  32. Tiwari RK, Beesham A, Shukla BK. Scenario of Two-Fluid Dark Energy Models in Bianchi Type-III Universe, Int. J. Geometric Methods in Modern Physics,2018:15:1850189.
  33. Naidu RL, Aditya Y, Reddy DRK. Bianchi Type-V Dark Energy Cosmological Model in General Relativity in the Presence of Massive Scalar Field, J. Heliyon, 2019, e01645, 2019.
  34. Beig R, Schmidt B. Time -Independent Gravitational Fields, Lect. Notes Phys.,2000:540:325-372.
  35. Garcia AA, Campuzano C. Conformally Flat Stationary Axisymmetric Space-times, Physical Review D,2002:66:124018.
  36. Wu X, Shang Y. On Newman-Penrose Constants of Stationary Space-times, 2006, arXiv: gr - qc/0612109v1.
  37. Katz J, Lynden-Bell D, Bicak J. Gravitational Energy in Stationary Space-times, J. Class. Quant. Grav.,2006:23:7111-7128.
  38. Javaloyes M. A. and Sanchez M., Existence of Standard Splittings for Conformally Stationary Space-times, J. Class. Quant. Grav.,2008:25:168001.
  39. Chrusciel PT, Delay E. Non -Singular, Vacuum, Stationary Space-times with a Negative Cosmological Constant, Annales Henri Poincare,2007:8:219-239, arXiv: gr-qc/0512110v2.
  40. Nayak KR. Einstein Equations and Inertial Forces in Axially Symmetric Stationary Space-times, Gen. Relativ. Gravit.,2009:41:2737-2756.
  41. Borkar MS, Dhongle PR. Bianchi Type I String Dust Model with Magnetic Field in Stationary Space-Time, Int. J. of Applied Mathematics,2010:23(6):977-988.
  42. Borkar MS, Dhongle PR. Cylindrically Symmetric Inhomogeneous String Cosmological Model with Magnetic Field in Stationary Space-Time, American J. Pure & Applied Mathematics,2013:2(1):37-42.
  43. Borkar MS, Dhongle PR. Pre -Hawking Radiating Gravitational Collapse in Stationary Space-Time, Int. J. Theoretical & Applied Sciences,2013:5(2):27-31.
  44. Dhongle PR. The de-Sitter Model with Dark Energy, J. Research in Applied Mathematics,2021:7(11):33- 39.
  45. Landau LD, Lifshitz EM. The Classical Theory of Fields, Fourth Revised English Edition, Pergamon Press, Oxford, 1975.
  46. Ellis GFR. General Relativity and Cosmology, ed. by R. K. Sachs, Academic Press, New York, 1971.