Eur. Phys. J. C (2014) 74:2760
DOI 10.1140/epjc/s10052-014-2760-3
Regular Article - Theoretical Physics
Dissipative spherical collapse of charged anisotropic fluid in f (R)
gravity
H. Rizwana Kausar
1,a
, Ifra Noureen
2,b
1
Centre for Applicable Mathematics and Statistics, University of Central Punjab, Lahore, Pakistan
2
University of Management and Technology, Lahore, Pakistan
Received: 18 January 2014 / Accepted: 27 January 2014 / Published online: 25 February 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract This manuscript is devoted to the study of the
combined effect of a viable f (R) = R +α R
n
model and the
electromagnetic field on the instability range of gravitational
collapse. We assume the presence of a charged anisotropic
fluid that dissipates energy via heat flow and discuss how
the electromagnetic field, density inhomogeneity, shear, and
phase transition of astrophysical bodies can be incorporated
by a locally anisotropic background. The dynamical equa-
tions help to investigate the evolution of self-gravitating
objects and lead to the conclusion that the adiabatic index
depends upon the electromagnetic background, mass, and
radius of the spherical objects.
1 Introduction
Gravitational collapse is a highly dissipative phenomenon.
The effects of dissipation describe a wide range of situations.
For example, using a quasi-static approximation, limit cases
of radiative transport have been studied in [1]. It is found
that the hydrostatic time scale is very small as compared to
the stellar lifetimes for different phases of a star’s life. It is
of the order of 27 min for the sun, 4.5 s for a white dwarf
and 10
−4
s for a neutron star of one solar mass and 10 km
radius [2–4]. The dissipative factors enhance the instability
range in the Newtonian limits but develop more stability in
relativistic ranges. The impressions of radiation, anisotropy,
and shearing viscosity at Newtonian and post-Newtonian eras
are inquired in [5–8]. Various prospects of the collapse phe-
nomenon to account for dark source have been worked out in
the recent past [9–14]. Due to a high dissipation, matter pro-
duces a large amount of charge in the collapse phenomenon
and so one is well motivated to investigate the effects of the
electromagnetic field on the gravitational collapse [15].
a
e-mail: rizwa_math@yahoo.com
b
e-mail: ifra.noureen@gmail.com
Chandrasekhar [16] took the initiative to work out the
dynamical instability problem. Dynamical instability is sig-
nificant in establishing the evolution and formation of stellar
objects that must be stable against fluctuations. Generally, the
adiabatic index is useful to address the instability problem.
The isotropic spheres of mass M and R radius may be related
by ≥
4
3
+n
M
r
, where the number n depends upon the star’s
structure. Later on the instability range for anisotropic, adi-
abatic, non-adiabatic, and shearing viscous fluids had been
examined in [17–19]. Besides , many other matter variables
such as dissipation, radiation, shearing stress, anisotropy,
expansion-free condition, etc. may also be responsible for
the dynamical instability and the evolution in stars depend-
ing upon the properties of t he fluid.
Modified theories of gravity have received enormous
attention in recent years. The inclusion of higher order cur-
vature invariants and coupled scalar fields has become a
paradigm in alternative gravity theories. For this purpose,
various alterations are made in the Einstein–Hilbert (EH)
action [20–22]. The elementary and likely modification is to
include curvature terms that are of type f (R) having combi-
nations of the Ricci scalar R. In this way, gravity tends to get
modified on large scales, which reveals enormous observa-
tional signatures like a modified galaxy clustering spectrum
[23,24], weak lensing [25,26], and the cosmic microwave
background [27,28].
The most studied and simplest models in f (R) theory are
f (R) = R+σ
μ
4
R
and f (R) = R+α R
2
, where σ =±1, α is
a positive real number and μ is a parameter with the units of
mass. Usually, positive values of the scalar curvature depicts
standard cosmological corrections lead to de Sitter space
[29], whereas negative values help to discuss the accelerating
universe due to dark energy [30]. The effects of these f (R)
models on the dynamical instability of gravitational collapse
has been discussed in recent papers [31,32]. In the same con-
text, Sharif and Yousaf established the range of instability for
a charged expansion-free, dissipative collapse for spherical
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