Abstract.
The present paper provides a new model of compact stars satisfying the Karmarkar condition. The model is obtained by assuming a new type of metric potential for \(g_{rr}\) from the condition of embedding class I. The model parameters are obtained accordingly by employing the metric potentials to Einstein's field equations. Our model is free from geometric singularity and satisfies all the physical conditions. The obtained mass and radius of the compact stars Cen X-3, EXO 1785-248 and SAX 1808.4-3658 obtained from the model are consistent with the observational data of T. Gangopadhyay et al.. Detailed analyses of these neutron stars (Cen X-3, EXO 1785-248 and SAX 1808.4-3658) are also given with the help of graphical representations.
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References
R. Ruderman, Annu. Rev. Astron. Astrophys. 10, 427 (1972)
V. Canuto, Annu. Rev. Astron. Astrophys. 12, 167 (1974)
V. Canuto, Annu. Rev. Astron. Astrophys. 13, 335 (1975)
V. Canuto, Ann. N. Y. Acad. Sci. U.S.A. 302, 514 (1977)
V. Canuto, M. Chitre, Phys. Rev. Lett. 30, 999 (1973)
V. Canuto, S.M. Chitre, Phys. Rev. D 9, 1587 (1974)
V. Canuto, J. Lodenquai, Phys. Rev. D 11, 233 (1975)
V. Canuto, J. Lodenquai, Phys. Rev. C 12, 2033 (1975)
R.L. Bowers, E.P.T. Liang, Astrophys. J. 188, 657 (1974)
M. Cosenza, L. Herrera, M. Esculpi, L. Witten, J. Math. Phys. 22, 118 (1981)
M. Cosenza, L. Herrera, M. Esculpi, L. Witten, Phys. Rev. D 25, 2527 (1982)
S.S. Bayin, Phys. Rev. D 26, 1262 (1982)
K.D. Krori, P. Borgohaiann, R. Devi, Can. J. Phys. 62, 239 (1984)
L. Herrera, J. Ponce de León, J. Math. Phys. 26, 2302 (1985)
J. Ponce de León, Gen. Relativ. Gravit. 19, 797 (1987)
J. Ponce de León, J. Math. Phys. 28, 1114 (1987)
H. Bondi, Mon. Not. R. Astron. Soc. 259, 365 (1992)
L. Herrera, N. Santos, Phys. Rep. 286, 53 (1997)
L. Herrera, A.D. Prisco, J. Ospino, E. Fuenmayor, J. Math. Phys. 42, 2129 (2001)
L. Herrera, J. Ospino, A.D. Prisco, Phys. Rev. D 77, 027502 (2008)
K. Dev, M. Gleiser, Gen. Relativ. Gravit. 34, 1793 (2002)
K. Dev, M. Gleiser, Gen. Relativ. Gravit. 35, 1435 (2003)
M. Gleiser, K. Dev, Int. J. Mod. Phys. D 13, 1389 (2004)
B.V. Ivanov, Phys. Rev. D 65, 104011 (2002)
M.K. Mak, T. Harko, Chin. J. Astron. Astrophys. 2, 248 (2002)
M.K. Mak, T. Harko, Proc. R. Soc. Lond. A 459, 393 (2003)
M.K. Mak, P.N. Dobson, T. Harko, Int. J. Mod. Phys. D 11, 207 (2002)
S. Viaggiu, Int. J. Mod. Phys. D 18, 275 (2009)
B.V. Ivanov, Int. J. Theor. Phys. 49, 1236 (2010)
S.D. Maharaj, R. Maartens, Gen. Relativ. Gravit. 21, 899 (1989)
M.K. Gokhroo, A.L. Mehra, Gen. Relativ. Gravit. 26, 75 (1994)
T. Singh, G.P. Singh, R.S. Srivastava, Int. J. Theor. Phys. 31, 545 (1992)
T. Singh, G.P. Singh, A.M. Helmi, Nuovo Cimento B 110, 387 (1995)
L.K. Patel, S.K. Vaidya, Acta Phys. Hung.: Heavy Ion Phys. 3, 177 (1996)
R. Tikekar, V.O. Thomas, Pramana J. Phys. 52, 237 (1999)
M.K. Mak, T. Harko, Int. J. Mod. Phys. D 13, 149 (2004)
M. Chaisi, S.D. Maharaj, Gen. Relativ. Gravit. 37, 1177 (2005)
M. Chaisi, S.D. Maharaj, Pramana J. Phys. 66, 609 (2006)
M. Chaisi, S.D. Maharaj, Pramana J. Phys. 66, 313 (2006)
S.D. Maharaj, M. Chaisi, Gen. Relativ. Gravit. 38, 1723 (2006)
S.D. Maharaj, M. Chaisi, Math. Meth. Appl. Sci. 29, 67 (2006)
R. Sharma, S.D. Maharaj, Mon. Not. R. Astron. Soc. 375, 1265 (2007)
V. Varela, F. Rahaman, S. Ray, K. Chakraborty, M. Kalam, Phys. Rev. D 82, 044052 (2010)
M. Esculpi, E. Alomá, Eur. Phys. J. C 67, 521 (2010)
K. Komathiraj, S.D. Maharaj, Int. J. Mod. Phys. D 16, 1803 (2011)
P.M. Takisa, S.D. Maharaj, Astrophys. Space Sci. 343, 569 (2012)
P.M. Takisa, S.D. Maharaj, Astrophys. Space Sci. 343, 569 (2013)
P.M. Takisa, S.D. Maharaj, Gen. Relativ. Gravit. 45, 1951 (2013)
S.D. Maharaj, P.M. Takisa, Gen. Relativ Gravit. 44, 1419 (2012)
T. Feroze, A.A. Siddique, Gen. Relativ. Gravit. 43, 1025 (2011)
T. Feroze, A.A. Siddique, J. Korean Phys. Soc. 65, 944 (2014)
T. Feroze, Can. J. Phys. 90, 1179 (2012)
T. Feroze, H. Tariq, Can. J. Phys. 93, 637 (2014)
F. Rahaman, R. Sharma, S. Ray, R. Maulick, I. Karar, Eur. Phys. J. C 72, 2071 (2012)
M. Kalam, A.A. Usmani, F. Rahaman, S.M. Hossein, I. Karar, R. Sharma, Int. J. Theor. Phys. 52, 3319 (2013)
S. Thirukkanesh, F.C. Ragel, Pramana J. Phys. 78, 687 (2012)
S. Thirukkanesh, F.C. Ragel, Pramana J. Phys. 81, 275 (2013)
S. Thirukkanesh, F.C. Ragel, Astrophys. Space Sci. 354, 415 (2014)
S. Thirukkanesh, F.C. Ragel, Astrophys. Space Sci. 352, 743 (2014)
S.A. Ngubelanga, S.D. Maharaj, S. Ray, Astrophys. Space Sci. 357, 40 (2015)
S.A. Ngubelanga, S.D. Maharaj, S. Ray, Astrophys. Space Sci. 357, 74 (2015)
S.K. Maurya, Y.K. Gupta, Phys. Scr. 86, 025009 (2012)
S.K. Maurya, Y.K. Gupta, Astrophys. Space Sci. 344, 243 (2013)
S.K. Maurya, Y.K. Gupta, Astrophys. Space Sci. 353, 657 (2014)
R. Sharma, B.S. Ratanpal, Int. J. Mod. Phys. D 22, 1350074 (2013)
S.D. Maharaj, J.M. Sunzu, S. Ray, Eur. Phys. J. Plus 129, 3 (2014)
J.M. Sunzu, S.D. Maharaj, S. Ray, Astrophys. Space Sci. 352, 719 (2014)
J.M. Sunzu, S.D. Maharaj, S. Ray, Astrophys. Space Sci. 354, 2131 (2014)
M.H. Murad, S. Fatema, Eur. Phys. J. C 75, 533 (2015)
M.H. Murad, S. Fatema, Eur. Phys. J. Plus 130, 3 (2015)
S.K. Maurya, Y.K. Gupta, S. Ray, B. Dayanandan, Eur. Phys. J. C 75, 225 (2015)
S. Thirukkanesh, M. Govender, D.B. Lortan, Int. J. Mod. Phys. D 24, 1550002 (2015)
D.M. Pandya, V.O. Thomas, R. Sharma, Astrophys. Space Sci. 356, 285 (2015)
P. Bhar, M.H. Murad, N. Pant, Astrophys. Space Sci. 359, 13 (2015)
P. Bhar, S.K. Maurya, Y.K. Gupta, T. Manna, Eur. Phys. J. A 52, 312 (2016)
K.R. Karmakar, Proc. Ind. Acad. Sci. A 27, 56 (1948)
Ksh. N. Singh, N. Pant, Astrophys. Space Sci. 361, 177 (2016)
Ksh. N. Singh, N. Pant, N. Pradhan, Astrophys. Space Sci. 361, 173 (2016)
Ksh. N. Singh, P. Bhar, N. Pant, Int. J. Mod. Phys. D 25, 1650099 (2016)
Ksh. Newton Singh, Piyali Bhar, and Neeraj Pant, Astrophys. Space Sci. 361, 339 (2016)
K.N. Singh, N. Pant, and M. Govender, Chin. Phys. C 41, 015103 (2017)
N. Pant, K.N. Singh, N. Pradhan, Indian J. Phys., DOI:10.1007/s12648-016-0917-7 (2016)
Ksh. Newton Singh, Neeraj Pant, Eur. Phys. J. C 76, 524 (2016)
S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 13, 113 (1982)
H. Abreu, H. Hernández, L.A. Núñez, Class. Quantum Grav. 24, 4631 (2007)
C.G. Böhmer, T. Harko, Class. Quantum Grav. 23, 6479 (2006)
T. Gangopadhyay, S. Ray, X.D. Li, J. Dey, M. Dey, Mon. Not. R. Astron. Soc. 431, 3216 (2013)
H.A. Buchdahl, Phys. Rev. 116, 1027 (1959)
N. Straumann, General Relativity and Relativistic Astrophysics (Springer-Verlag, Berlin, Heidelberg, 1984)
R. Chan, L. Herrera, N.O. Santos, Class. Quantum Grav. 9, L133 (1992)
H. Bondi, Proc. R. Soc. Lond. A 281, 39 (1964)
L. Herrera, Phys. Lett. A 165, 206 (1992)
R. Chan, L. Herrera, N.O. Santos, Mon. Not. R. Astron. Soc. 265, 533 (1993)
L. Herrera, J. Ospino, A. Di Prisco, Phys. Rev. D 77, 027502 (2008)
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Singh, K.N., Murad, M.H. & Pant, N. A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars. Eur. Phys. J. A 53, 21 (2017). https://doi.org/10.1140/epja/i2017-12210-1
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DOI: https://doi.org/10.1140/epja/i2017-12210-1