Eur. Phys. J. C (2020) 80:119
https://doi.org/10.1140/epjc/s10052-020-7647-x
Regular Article - Theoretical Physics
Impact of generalized polytropic equation of state on charged
anisotropic polytropes
S. A. Mardan
a
, M. Rehman
b
, I. Noureen
c
,R.N.Jamil
d
Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore, Pakistan
Received: 28 August 2019 / Accepted: 13 January 2020
© The Author(s) 2020
Abstract In this paper, generalized polytropic equation of
state is used to get new classes of polytropic models from
the solution of Einstein-Maxwell field equations for charged
anisotropic fluid configuration. The models are developed
for different values of polytropic index n = 1,
1
2
, 2. Masses
and radii of eight different stars have been regained with the
help of developed models. The speed of sound technique and
graphical analysis of model parameters is used for the via-
bility of developed models. The analysis of models indicates
they are well behaved and physically viable.
1 Introduction
Polytropes are very useful to study the internal structure of
stars. They can be used to discuss various astronomical sit-
uations and description of compact objects. Chandrasekhar
[1] developed the basic theory of Newtonian polytropes by
using laws of thermodynamics for polytropic spheres. Tooper
[2] derived hydrostatic equilibrium equations for spherically
symmetric objects and obtained numerical solutions for adia-
batic process with compressible fluid. Irregularities arised in
Chandrasekhar’s theory of slowly rotating polytropes were
removed by Kovetz [3]. Generalized forms of Lane-Emden
equation (LEe) for cylindrical, spherical and planer poly-
tropes were derived by Abramowicz [4]. Ngubelanga and
Maharaj [5] obtained new classes of polytropic models for
different values of polytropic index. Isayev [6] discussed gen-
eral relativistic polytropes in anisotropic stars and derived
generalized LEe for arbitrary anisotropic parameter.
The discussion of anisotropy factor is essential while
studying the formation of stars. Bowers and Liang [7] high-
lights the importance of locally anisotropic equation of state
a
e-mail: syedalimardanazmi@yahoo.com
b
e-mail: f2016109014@umt.edu.pk
c
e-mail: ifra.noureen@gmail.com
d
e-mail: noshad.jamil@umt.edu.pk
by generalizing the equation of hydrostatic equilibrium. The
change in maximum equilibrium mass and red-shift was
found proportional to anisotropic factor. Dev and Gleiser
[8] studied effects of pressure anisotropy on stars and found
that it has significant effects on the structure and properties.
Maurya and Gupta [9] developed a family of anisotropic
fluid distributions using spherically symmetric space-time
to describe a family of charged perfect fluid distributions.
Thirukkanesh and Ragel [10] studied the properties of stellar
objects having anisotropic distribution in spherically sym-
metric space-time. Mardan et al. [11] investigated the gravita-
tional behavior of stellar objects by new classes of anisotropic
polytropes for different values of polytropic index. They used
GPEoS with anisotropic matter distributions and considered
quadratic form of gravitational potential to get the solutions
of Einstein field Equations (EFE).
It is important to discuss effects of charge in stellar mod-
els for many applications. The effects of electronic forces
in hydrostatic equilibrium state of charged stars were ini-
tially discussed by Rosseland [12]. Bonner [13,14] stud-
ied the effect of charge on spherically symmetric stellar
objects and found that electric repulsion can halt the gravita-
tional collapse. Sharma et al. [15] solved field equations for
charged sphere by taking a special class of hyper-surfaces
and more general behavior of charged spheres was observed
than uncharged spheres. They also presented the presence of
charge over wide range of parameters. The red shift, luminos-
ity and mass of the stellar objects were affected in the pres-
ence of electric field was presented by Ivanov [16]. Ray et
al. [17] analyzed the effect of charge in astronomical objects
and found the maximum charge a star can hold is about 10
20
Coulomb. Thirukkanesh and Maharaj [18] obtained solution
of field equations in presence electromagnetic field which
described anisotropic compact objects having properties sim-
ilar to SAX J1808.4-3658, a star. To obtain exact solutions for
field equations with anisotropic pressure and electromagnetic
field Takisa and Maharaj [19] used the polytropic equation of
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