Research PapersNo Access

A new class of relativistic model of compact stars of embedding class I

Piyali Bhar

Department of Mathematics, Government General Degree College, Singur, Hooghly, West Bengal 712409, India

E-mail Address: piyalibhar90@gmail.com

Search for more papers by this author

Ksh. Newton Singh

Department of Physics, National Defence Academy, Khadakwasla, Pune 411023, India

E-mail Address: ntnphy@gmail.com

Search for more papers by this author

, and

Tuhina Manna

Department of Commerce (Evening), St. Xavier’s College, 30 Mother Teresa Sarani, Kolkata 700016, West Bengal, India

E-mail Address: tuhinamanna03@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0218271817500900Cited by:51 (Source: Crossref)

Abstract

In the present paper, we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function $e^{λ}$ $e^{λ}$ and solved the Einstein’s relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational redshift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion, i.e. $d M / d ρ_{c} > 0$ $d M / d ρ_{c} > 0$ for $0 \leq ρ_{c} \leq 4.04 \times 1 0^{17}$ $0 \leq ρ_{c} \leq 4.04 \times 1 0^{17}$ g/cm³ (stable region) and for $ρ_{c} \geq 4.04 \times 1 0^{17}$ $ρ_{c} \geq 4.04 \times 1 0^{17}$ g/cm³, the region is unstable i.e. $d M / d ρ_{c} \leq 0$ $d M / d ρ_{c} \leq 0$ .

Keywords:

PACS: 04.40.Nr, 04.20.Jb, 04.20.Dw

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55 (1939) 374. ADS, Google Scholar
2. R. C. Tolman, Phys. Rev. 55 (1939) 364. ADS, Google Scholar
3. R. Ruderman, Annu. Rev. Astron. Astrophys. 10 (1972) 427. Web of Science, ADS, Google Scholar
4. R. Kippenhahm and A. Weigert, Stellar Structure and Evolution (Springer, Berlin, 1990). Google Scholar
5. A. I. Sokolov, JETP 52 (1980) 575. ADS, Google Scholar
6. R. F. Sawyer, Phys. Rev. Lett. 29 (1972) 382, Erratum 667 (1972) 823. Google Scholar
7. J. Ponce de León, Gen. Rel. Gravit. 25 (1993) 1123. Web of Science, Google Scholar
8. L. Herrera, Phys. Lett. A 165 (1992) 206. Web of Science, ADS, Google Scholar
9. C. G. Böhmer and T. Harko, arXiv:gr-qc:0609061v1. Google Scholar
10. M. K. Mak and T. Harko, Proc. R. Soc. A 459 (2003) 393. ADS, Google Scholar
11. R. Sharma, S. Mukherjee and S. D. Maharaj, Gen. Relativ. Gravit. 33 (2001) 999. Web of Science, ADS, Google Scholar
12. P. Bhar, Astrophys. Space Sci. 356 (2015) 309. Web of Science, ADS, Google Scholar
13. P. Bhar, Astrophys. Space Sci. 357 (2015) 46. Web of Science, ADS, Google Scholar
14. P. Bhar, Astrophys. Space Sci. 359 (2015) 41. Web of Science, ADS, Google Scholar
15. P. Bhar, M. H. Murad and N. Pant, Astrophys. Space Sci. 359 (2015) 13. Web of Science, ADS, Google Scholar
16. K. Nozari and S. H. Mehdipour, JHEP 0903 (2009) 061. Web of Science, ADS, Google Scholar
17. P. Bhar, F. Rahaman, S. Ray and V. Chatterjee, Eur. Phys. J. C 75 (2015) 190. Web of Science, ADS, Google Scholar
18. V. Varela, F. Rahaman, S. Ray, K. Chakraborty and K. Kalam, Phys. Rev. D 82 (2010) 044052. Web of Science, ADS, Google Scholar
19. M. Kalam, F. Rahaman, M. Hossein and S. Ray, Eur. Phys. J. C 73 (2013) 2409. Web of Science, ADS, Google Scholar
20. M. Hossein, F. Rahaman, J. Naskar, M. Kalam and S. Ray, Int. J. Mod. Phys. D 21 (2012) 1250088. Link, Web of Science, ADS, Google Scholar
21. F. Rahaman et al., Phys. Rev. D 82 (2010) 104055. Web of Science, ADS, Google Scholar
22. K. Schwarzschild, Sitz. Deut. Akad. Wiss. Math.-Phys. Berlin 24 (1916) 424. Google Scholar
23. M. Kohler and K. L. Chao, Z. Naturforsch. Ser. A 20 (1965) 1537. ADS, Google Scholar
24. P. Bhar, S. K. Maurya, Y. K. Gupta and T. Manna, Eur. Phys. J. A 52 (2016) 312. Web of Science, ADS, Google Scholar
25. S. K. Maurya, Y. K. Gupta, T. T. Smitha and F. Rahaman, Eur. Phys. J. A 52 (2016) 191. Web of Science, ADS, Google Scholar
26. S. K. Maurya, Y. K. Gupta, B. Dayanandan and S. Ray, Eur. Phys. J. C 76 (2016) 266. Web of Science, ADS, Google Scholar
27. S. K. Maurya, Y. K. Gupta, S. Ray and B. Dayanandan, Eur. Phys. J. C 75 (2015) 225. Web of Science, ADS, Google Scholar
28. K. N. Singh and N. Pant, Astrophys. Space Sci. 361 (2016) 177. Web of Science, ADS, Google Scholar
29. K. N. Singh et al., Astrophys. Space Sci. 361 (2016) 173. Web of Science, ADS, Google Scholar
30. K. N. Singh et al., Int. J. Mod. Phys. D 25 (2016) 1650099. Link, Web of Science, ADS, Google Scholar
31. K. N. Singh and N. Pant, Eur. Phys. C 76 (2016) 524. Web of Science, ADS, Google Scholar
32. K. N. Singh et al., Chin. Phys. C 41 (2017) 015103. Web of Science, Google Scholar
33. N. Pant et al., Ind. J. Phys. 91 (2017) 343. Web of Science, Google Scholar
34. K. R. Karmarkar, Proc. Ind. Acad. Sci. A 27 (1948) 56. Google Scholar
35. S. N. Pandey and S. P. Sharma, Gen. Relativ. Gravit. 14 (1982). Web of Science, Google Scholar
36. H. Abreu, H. Hernández and L. A. Núñez, Class. Quantum Grav. 24 (2007) 4631. Web of Science, ADS, Google Scholar
37. R. L. Bowers and E. P. T. Liang, Astrophys. J. 188 (1974) 657. Web of Science, ADS, Google Scholar
38. B. V. Ivanov, Phys. Rev. D 65 (2002) 104011. Web of Science, ADS, Google Scholar
39. C. G. Böhmer and T. Harko, Class. Quantum Grav. 23 (2006) 6479. Web of Science, ADS, Google Scholar
40. M. K. Gokhroo and A. L. Mehra, Gen. Relativ. Gravit. 26 (1994) 75. Web of Science, ADS, Google Scholar
41. H. A. Buchdahl, Phys. Rev. 116 (1959) 1027. Web of Science, ADS, Google Scholar
42. R. Chan, L. Herrera and N. O. Santos, Mon. Not. R. Astron. Soc. 265 (1993) 533. Web of Science, ADS, Google Scholar
43. H. Bondi, Proc. R. Soc. Lond. A 281 (1964) 39. Web of Science, ADS, Google Scholar
44. L. Herrera, Phys. Lett. A 165 (1992) 206. Web of Science, ADS, Google Scholar
45. H. Andréasson, Commun. Math. Phys. 288 (2009) 715. Web of Science, ADS, Google Scholar
46. S. Chandrasekhar, Phys. Rev. Lett. 12 (1964) 114. Web of Science, ADS, Google Scholar
47. B. K. Harrison et al., Gravitational Theory and Gravitational Collapse (University of Chicago Press, Chicago, 1965). Google Scholar
48. Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics Vol. 1: Stars and Relativity (University of Chicago Press, Chicago, 1971). Google Scholar
49. M. L. Rawls, J. A. Orosz, J. E. McClintock, M. A. P. Torres, C. B. Bailyn and M. M. Buxton, Astrophys. J. 730 (2011) 25. Web of Science, ADS, Google Scholar
50. Freire et al., Mon. Not. R. Astron. Soc. 412 (2011) 2763. Web of Science, ADS, Google Scholar
51. T. Gangopadhyay et al., Mon. Not. R. Astron. Soc. 431 (2013) 3216. Web of Science, ADS, Google Scholar