A New Classes of Solutions of the Einstein-Maxwell Field Equations with Pressure Anisotropy

Subject Areas : International Journal of Mathematical Modelling & Computations

Kalikkuddy Komathiraj ^{1 *}

1 - Department of Mathematical Science, Faculty of Applied Sciences, South Eastern University of Sri Lanka, Sri Lanka

Received: 2023-04-04 Accepted : 2023-06-20 Published : 2023-06-01

Keywords: Exact solutions, Relativistic star, field equations, astrophysical objects,

Abstract :

In this paper, we present a class of exact solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere. The field equations are integrated by specifying the forms of the electric field, anisotropic factor, and one of the gravitational potentials which are physically reasonable. By reducing the condition of pressure isotropy to a linear, second order differential equation which can be solved in general, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. The solution is regular, well behaved and complies with all the requirements of a realistic stellar model. An interesting feature of the new class of solutions is that one can easily switch off the electric and/or anisotropic effects in this formulation. Consequently, we regain some of the earlier solutions.

References:

References
[1] Ivanov B. V., Static charged perfect fluid spheres in general relativity. Physical Review D 65 (2002) 104001.
[2] Bowers R. L. and Liang, E. P. T., Anisotropic spheres in general relativity. The Astrophysical Journal 188 (1974) 657–665.
[3] Dev K. and Gliser M., Anisotropic stars: Exact solutions. General Relativity and Gravitation 34 (2002) 1793–1818.
[4] Paul B. C., Chattopadhyay P. K., Karmakar S. and Tikekar R., Relativistic strange stars with anisotropy. Modern Physics Letter A 26 (2011) 575-587.
[5] Herrera L. and Santos N. O., Local anisotropy in self-gravitating systems. Phys. Rep. 286 (1997) 53-130.
[6] Komathiraj K., Sharma R., Das S. and Maharj S. D., Generalized Durgapal–Fuloria relativistic stellar models. Journal of Astrophysics and Astronomy (2019) 40, 37.
[7] Komathiraj K. and Sharma R., Effects of electric field and anisotropy on the mass-radius relationship of a particular class of compact stars. Astrophysics and Space Science (2022) 367, 86.
[8] Malaver, M., Strange Quark Star model with quadratic equation of state. Frontiers of Mathematics and its applications, 1(1) (2014) 9-15. https://arxiv.org/abs/1407.0760
[9] Malaver, M., Quark star model with charge distributions. Open Science Journal of Modern Physics, 1(1) (2014) 6-11. https://arxiv.org/abs/1407.1936
[10] Malaver, M., Models for quark stars with charged anisotropic matter. Research Journal of Modeling and Simulation, 1(4) (2014) 65-71.
https://arxiv.org/abs/1410.1524
[11] Malaver M., Charged anisotropic models in a modified Tolman IV spacetime. World Scientific News 101 (2018) 31–43.
[12] Malaver, M., Charged anisotropic matter with modified Tolman IV potential. Open Science Journal of modern physics 2(5) (2015), 65-71.
[13] Malaver M., Some new models of anisotropic compact stars with quadratic equation of state. World Scientific News 109 (2018) 180–194.
[14] Malaver M. and Kasmaei H. D., Charged anisotropic matter with modified Chaplygin equation of state. International Journal of Physics: Study and Research 3 (2021) 83–90.
[15] Malaver M. and Kasmaei H. D., Classes of charged anisotropic stars with polytropic equation of state. IJRRAS 46 (2021).
[16] Malaver M. and Kasmaei H. D., Analytical models for quark stars with Van der Waals modified equation of state. International Journal of Astrophysics and Space Science 7 (2019) 49–58.
[17] Malaver M. and Kasmaei H. D., Relativistic stellar models with quadratic equation of state. International Journal of Mathematical Modelling & Computations 10 (2020) 111–124.
[18] Komathiraj K., Anisotropic Charged Stellar Models. International Journal of Mathematical Modelling Computations 12 (2022) 51–60.
[19] Durgapal M. C. and Bannerji R., New analytical stellar model in general relativity. Physical Review D 27 (1983) 328–331.
[20] Komathiraj K. and Maharaj S. D., Classes of exact Einstein-Maxwell solutions. General Relativity and Gravitation 39 (2007) 2079–2093.
[21] Thirukkanesh S. and Maharaj S. D., Some new static charged spheres. Nonlinear Analysis: Real World Applications 10 (2009) 3396–3403.
[22] Delgaty M. S. R. and Lake K., Physical acceptability of isolated, static, spherically symmetric, perfect fluid solutions of Einstein's equations. Computational Physics and Communication 115 (1998) 395- 415.
[23] Komathiraj K. and Sharma R., Generating new class of exact solutions to the Einstein– Maxwell system. European Physical Journal Plus 136 (2021) 352