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General relativistic effects in the structure of massive white dwarfs. (English) Zbl 1392.83012
Summary: In this work we investigate the structure of white dwarfs using the Tolman-Oppenheimer-Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of general relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs (\(M>1.3M_{\odot}\)) are overestimated in comparison with GR outcomes. For a mass of \(1.415M_{\odot}\) the white dwarf radius predicted by GR is about 33% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65%. We depict the general relativistic mass-radius diagrams as \(M/M_{\odot}=R/(a+bR+cR^2+dR^3+kR^4)\), where \(a\), \(b\), \(c\) and \(d\) are parameters obtained from a fitting procedure of the numerical results and \(k=(2.08\times 10^{-6}R_{\odot})^{-1}\), being \(R_{\odot}\) the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.

MSC:
83C15 Exact solutions to problems in general relativity and gravitational theory
85A15 Galactic and stellar structure
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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References:
[1] Kepler, SO; etal., No article title, Mon. Not. R. Astron. Soc., 375, 1315, (2007)
[2] Kleinman, SJ; etal., No article title, Astrophys. J. Suppl. Ser., 204, 5, (2013)
[3] Należyty, M; Madej, J, No article title, Astron. Astrophys., 420, 507, (2004)
[4] Vennes, S; etal., No article title, Astrophys. J., 480, 714, (1997)
[5] Chandrasekhar, S, No article title, Mon. Not. R. Astron. Soc., 95, 207, (1935) · Zbl 0011.08503
[6] Hicken, M; etal., No article title, Astrophys. J. Lett., 669, l17, (2007)
[7] Yamanaka, M; etal., No article title, Astrophys. J. Lett., 707, l118, (2009)
[8] Scalzo, RA; etal., No article title, Astrophys. J., 713, 1073, (2010)
[9] Taubenberger, S; etal., No article title, Mon. Not. R. Astron. Soc., 412, 2735, (2011)
[10] Leibundgut, B, No article title, Gen. Relativ. Gravit., 40, 221, (2008) · Zbl 1137.85331
[11] Howell, DA; etal., No article title, Nature, 443, 308, (2006)
[12] Silverman, JM; etal., No article title, Mon. Not. R. Astron. Soc., 410, 585, (2010)
[13] Franzon, B; Schramm, S, No article title, Phys. Rev. D, 92, 083006, (2015)
[14] Otoniel, E; etal., No article title, Int. J. Mod. Phys. Conf. Ser., 45, 1760024, (2017)
[15] Das, U; Mukhopadhyay, B, No article title, J. Cosmol. Astropart. Phys., 2014, 050, (2014)
[16] Das, U; Mukhopadhyay, B, No article title, J. Cosmol. Astropart. Phys., 2015, 016, (2015)
[17] Bera, P; Bhattacharya, D, No article title, Mon. Not. R. Astron. Soc., 445, 3951, (2014)
[18] Coelho, JG; etal., No article title, Astrophys. J., 794, 6, (2013)
[19] Lobato, RV; Malheiro, M; Coelho, JG, No article title, Int. J. Mod. Phys. D, 25, 1641025, (2016)
[20] Malheiro, M; Rueda, JA; Ruffini, R, No article title, Publ. Astron. Soc. Jpn., 64, 56, (2012)
[21] Rueda, JA; etal., No article title, Astrophys. J. Lett., 772, l24, (2013)
[22] Coelho, JG; Malheiro, M, No article title, Publ. Astron. Soc. Jpn., 66, 14, (2014)
[23] Mukhopadhyay, B; Rao, A, No article title, J. Cosmol. Astropart. Phys., 2016, 007, (2016)
[24] Cáceres, DL; etal., No article title, Mon. Not. R. Astron. Soc., 465, 4434, (2017)
[25] Kaplan, SA, No article title, Naukovy Zapiski (Sci. Notes Univ. Lwow), 15, 109, (1949)
[26] Chandrasekhar, S; Tooper, RF, No article title, Astrophys. J., 139, 1396, (1964) · Zbl 0124.22102
[27] Cohen, J; Lapidus, A; Cameron, A, No article title, Astrophys. Space Sci., 5, 113, (1969)
[28] Boshkayev, K; etal., No article title, Astrophys. J., 762, 117, (2013)
[29] Boshkayev, K; Rueda, J; Ruffini, R, No article title, Int. J. Mod. Phys. E, 20, 136, (2011)
[30] Boshkayev, K; etal., No article title, J. Korean Phys. Soc., 65, 855, (2014)
[31] Boshkayev, K., et al.: General Relativistic and Newtonian White Dwarfs, pp. 2468-2474. World Scientific, Singapore (2015)
[32] Sagert, I; etal., No article title, Eur. J. Phys., 27, 577, (2006)
[33] Mathew, A; Nandy, MK, No article title, Res. Astron. Astrophys., 17, 061, (2017)
[34] Bera, P; Bhattacharya, D, No article title, Mon. Not. R. Astron. Soc., 456, 3375, (2016)
[35] Rotondo, M; Rueda, JA; Ruffini, R; Xue, SS, No article title, Phys. Rev. C, 83, 045805, (2011)
[36] Rotondo, M; Rueda, JA; Ruffini, R; Xue, SS, No article title, Phys. Rev. D, 84, 084007, (2011)
[37] Chandrasekhar, S.: An Introduction to the Study of Stellar Structure. Astrophysical Monographs. Dover Publications, New York (1957) · Zbl 0079.23901
[38] Rey, AU; Martínez, AP; Sussman, RA, No article title, Gen. Relativ. Gravit., 40, 1499, (2008) · Zbl 1148.83328
[39] Salpeter, EE, No article title, Astrophys. J., 134, 669, (1961)
[40] Hamada, T; Salpeter, EE, No article title, Astrophys. J., 134, 683, (1961)
[41] Adler, R., Bazin, M., Schiffer, M.: Introduction to General Relativity. McGraw-Hill, New York (1965) · Zbl 0144.47604
[42] Oppenheimer, JR; Volkoff, GM, No article title, Phys. Rev., 55, 374, (1939) · Zbl 0020.28501
[43] Tolman, RC, No article title, Phys. Rev., 55, 364, (1939) · Zbl 0020.28407
[44] Gautreau, R, No article title, Gen. Relativ. Gravit., 22, 671, (1990)
[45] Herrera, L, No article title, Gen. Relativ. Gravit., 35, 437, (2003) · Zbl 1016.83026
[46] Penrose, R, No article title, Gen. Relativ. Gravit., 34, 1141, (2002) · Zbl 1001.83040
[47] Knutsen, H, No article title, Gen. Relativ. Gravit., 20, 317, (1988) · Zbl 0636.76135
[48] Carvalho, GA; Marinho, RM; Malheiro, M, No article title, J. Phys. Conf. Ser., 630, 012058, (2015)
[49] Carvalho, G.A., Marinho Jr., R.M. Malheiro, M.: In: WSCP Proceedings of the Second Icranet César Lattes Meeting, p. 6 (2016)
[50] Ji, P; Qu, S; Bai, Y, No article title, Gen. Relativ. Gravit., 40, 131, (2008) · Zbl 1135.85001
[51] Carvalho, SM; Rotondo, M; Rueda, JA; Ruffini, R, No article title, Phys. Rev. C, 89, 015801, (2014)
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