The Modified Tolman-Oppenheimer-Volkov (TOV) Equation and the Effect of Charge on Pressure in Charge Anisotropy
American Journal of Physics and Applications
Volume 4, Issue 2, March 2016, Pages: 57-63
Received: Mar. 24, 2016; Published: Mar. 25, 2016
Views 3874      Downloads 144
Authors
Petarpa Boonserm, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Napasorn Jongjittanon, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Tritos Ngampitipan, Faculty of Science, Chandrakasem Rajabhat University, Bangkok, Thailand
Article Tools
Follow on us
Abstract
The Tolman-Oppenheimer-Volkov (TOV) equation describes the interior properties of spherical static perfect fluid object as a relationship between two physical observables - pressure and density. For a fluid sphere object, which contains electric charge, magnetic field, and scalar field, the pressure becomes anisotropic. In the previous article [Phys. Rev. D 76 (2007) 044024; gr-qc/0607001], we deformed TOV in terms of δρC and δpC, and we found a new physical and mathematical interpretation for the TOV equation. In this work, we cannot use the perfect fluid constrains because of the electromagnetic field and the massless scalar field within this object. The TOV equation was thus generalized to involve the electromagnetic and the scalar fields. This model is close to the realistic objects in our universe such as a neutron star. In this paper, we consider the modified TOV equation for Schwarzschild coordinates in a special case. The density is considered as a constant and the scalar field is considered absent. On the general model of the TOV equation, the pressure is expressed in terms of radius. However, this model shows that pressure is affected by electric charge. Moreover, we also calculate the rigorous bound on the transmission probability for the Tolman-Bayin type of charged fluid sphere.
Keywords
General Relativity, Modified TOV Equation, Charge Anisotropy, Transmission Probability
To cite this article
Petarpa Boonserm, Napasorn Jongjittanon, Tritos Ngampitipan, The Modified Tolman-Oppenheimer-Volkov (TOV) Equation and the Effect of Charge on Pressure in Charge Anisotropy, American Journal of Physics and Applications. Vol. 4, No. 2, 2016, pp. 57-63. doi: 10.11648/j.ajpa.20160402.14
References
[1]
M. S. R. Delgaty and K. Lake, “Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein’s equations”, Compute. Phys. Commun. 115 (1998) 395 [arXiv: gr-qc/9809013].
[2]
S. Rahman and M. Visser, “Spacetime geometry of static fluid spheres”, Class. Quant. Grav. 19 935 2002 [arXiv: gr-qc/0103065].
[3]
P. Boonserm, M. Visser and S. Weinfurtner, “Generating perfect fluid spheres in general relativity”, Phys. Rev. D 71 (2005) 124037 [arXiv: gr-qc/0503007].
[4]
P. Boonserm, M. Visser and S. Weinfurtner, “Solution generating theorems for the TOV equation”, Phys. Rev. D 76 (2007) 044024 [arXiv: gr-qc/0607001].
[5]
D. Martin and M. Visser, “Bounds on the interior geometry and pressure profile of static fluid spheres,” Class. Quant. Grav. 20 (2003) 3699-3716 [arXiv: gr-qc/ 0306038].
[6]
K. Lake, “All static spherically symmetric perfect fluid solutions of Einstein’s Equations,” Phys. Rev. D 67 (2003) 104015 [arXiv: gr-qc/0209104].
[7]
D. Martin and M. Visser, “Algorithmic construction of static perfect fluid spheres,” Phys. Rev. D 69 (2004) 104028 [arXiv: gr-qc/0306109].
[8]
S. Ray, A. L. Esp´indola, M. Malheiro, J. P. S. Lemos, and V. T. Zanchin, "Electrically charged compact stars and formation of charged black holes", Phys. Rev. D 68 084004, 2003 [arXiv: astro-ph/0307262].
[9]
W. Barreto, L. Castillo, and E. Barrios, “Central equation of state in spherical characteristic evolutions”, Phys. Rev. D 80 084007 2009 [arXiv: 0909.4500 [gr-qc]].
[10]
P. Boonserm, T. Ngampitipan and M. Visser, “Mimicking static anisotropic fluid spheres in general relativity”, International Journal of Modern Physics D (2015): 1650019 [arXiv: 1501.07044v3 [gr-qc]].
[11]
F. Siebel, J. A. Font, and P. Papadopoulos, “Scalar field induced oscillations of neutron stars and gravitational collapse”, Phys. Rev. D 65 024021 2001 [arXiv: gr-qc/0108006].
[12]
K. Schwarzschild, “On the gravitational field of a sphere of incompressible fluid according to Einstein’s theory”, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1916 (1916) 424 [arXiv: physics/9912033 [physics.hist-ph]].
[13]
S. Carroll, “Spacetime and geometry: an introduction to general relativity”, Pearson new international edition, U.S.A., Pearson Education Limited, 2014.
[14]
H. Bondi, “Spherically symmetrical models in general relativity”, Mon. Not. Roy. Astron. Soc. 107 (1947) 410.
[15]
H. A. Buchdahl, “General relativistic fluid spheres”, Phys. Rev. 116 (1959) 1027-1034.
[16]
A. Sulaksono, “Anisotropic pressure and hyperon in neutron stars,” Int. J. Mod. Phys. E 24 (2015) 01, 1550007 [arXiv: 1412.7274 [nucl-tn]].
[17]
P. Boonserm, “Some exact solution in general relativity”, MSc. Thesis, Victoria University of Wellington, 2006.
[18]
D Kramer, H Stephani, E Herlt, and M MacCallum, “Exact solutions of Einstein’s field equations”, (Cambridge University Press, England, 1980).
[19]
S. Ray, A. L. Esp´indola, M. Malheiro, J. P. S. Lemos, and V. T. Zanchin, "Electrically charged compact stars and formation of charged black holes", Phys. Rev. D 68 084004, 2003 [arXiv: astro-ph/0307262].
[20]
W. Barreto, L. Castillo, and E. Barrios, “Central equation of state in spherical characteristic evolutions”, Phys. Rev. D 80 084007 2009 [arXiv: 0909.4500 [gr-qc]].
[21]
L. Herrera, J. Ospino and A. Di Prisco, “All static spherically symmetric anisotropic solutions of Einstein’s equation”, Phys. Rev. D 77 (2008) 027502 [arXiv: 0712.0713 [gr-qc]].
[22]
Chandrasekhar, S. (1998). The Mathematical Theory of Black Holes (Reprinted ed.). Oxford University Press. p. 205. ISBN 0-19850370-9. Retrieved 13 May 2013.
[23]
P. Boonserm, and M. Visser, “Bounding the greybody factors for Schwarzschild black holes.” Phys. Rev. D 78(10) 101502 2008.
[24]
T. Ngampitipan, “Rigurous bounds on grey body factors for various types of black holes”, Ph. D. Thesis, Chulalongkorn University, 2014.
[25]
P. Boonserm, “Rigorous Bounds on Transmission, Reflection, and Bogoliubov Coefficients”, Ph. D. Thesis, Victoria University of Wellington (2009) [arXiv: 0907.0045 [mathph]].
[26]
Ray, Saibal, and Basanti Das, “Tolman-Bayin type static charged fluid spheres in general relativity.” Monthly Notices of the Royal Astronomical Society 349.4 (2004), 1331-1334.
[27]
P. Boonserm, A. Chatrabhuti, T. Ngampitipan, and M. Visser, “Greybody factors for Myers–Perry black holes”, J. Math. Phys. 55, 112502 (2014) [arXiv: 1405.5678[gr-qc]].
[28]
K. Komathiraj ans S. D. Maharaj, “A class of charged relativistic spheres”, Mathematical and Computational Applications 15, 665-673, 2010.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186