Eur. Phys. J. C (2016) 76:654
DOI 10.1140/epjc/s10052-016-4503-0
Regular Article - Theoretical Physics
Compact stars in f (R, T ) gravity
Amit Das
1,a
, Farook Rahaman
2,b
,B.K.Guha
1,c
, Saibal Ray
3,d
1
Department of Physics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
2
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700032, India
3
Department of Physics, Government College of Engineering and Ceramic Technology, Kolkata, West Bengal 700010, India
Received: 31 July 2016 / Accepted: 8 November 2016 / Published online: 28 November 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract In the present paper we generate a set of solu-
tions describing the interior of a compact star under f (R, T )
theory of gravity which admits conformal motion. An exten-
sion of general relativity, the f (R, T ) gravity is associated
to Ricci scalar R and the trace of the energy-momentum ten-
sor T . To handle the Einstein field equations in the form of
differential equations of second order, first of all we adopt
the Lie algebra with conformal Killing vectors (CKV) which
enable one to get a solvable form of such equations and sec-
ond we consider the equation of state (EOS) p = ωρ with
0 <ω<1 for the fluid distribution consisting of normal
matter, ω being the EOS parameter. We therefore analyti-
cally explore several physical aspects of the model to repre-
sent behavior of the compact stars such as—energy condi-
tions, TOV equation, stability of the system, Buchdahl condi-
tion, compactness and redshift. It is checked that the physical
validity and the acceptability of the present model within the
specified observational constraint in connection to a dozen
of the compact star candidates are quite satisfactory.
1 Introduction
Though Einstein’s general theory of relativity has always
proved to be very fruitful for uncovering so many hidden
mysteries of Nature, yet the evidence of late-time accelera-
tion of the Universe and the possible existence of dark mat-
ter has imposed a fundamental theoretical challenge to this
theory [1–7]. As a result, several modified theories on grav-
itation have been proposed from time to time. Among all
these theories, a few of them, namely f (R) gravity, f (T )
gravity and f (R, T ) gravity, have received more attention
a
e-mail: amdphy@gmail.com
b
e-mail: rahaman@associates.iucaa.in
c
e-mail: bkguhaphys@gmail.com
d
e-mail: saibal@associates.iucaa.in
than any other. In all these theories instead of changing the
source side of the Einstein field equations, the geometrical
part has been changed by taking a generalized functional
form of the argument to address galactic, extra-galactic, and
cosmic dynamics. Cosmological models based upon modi-
fied gravity theories reveal that excellent agreement between
theory and observation can be obtained [8–11].
In f (R) gravity theory the gravitational part in the stan-
dard Einstein–Hilbert action is replaced by an arbitrary gen-
eralized function of the Ricci scalar R whereas in f (T ) grav-
ity theory the same is replaced by an arbitrary analytic func-
tion of the torsion scalar T .The f (T ) theory of gravity is
more controllable than the f (R) theory of gravity because
the field equations in the former turns out to be the differ-
ential equations of second order whereas in the latter the
field equations in the form of differential equations are, in
general, of fourth order, which is difficult to handle [12].
Many applications of f (T ) gravity in cosmology, theoreti-
cal presentation as well as observational verification, can be
found in Refs. [13–28]. On the other hand, many astrophysi-
cal applications of f (T ) theory of gravity can be observed in
Refs. [12,29–33]. Following the result of Böhmer et al. [12]
in our previous work [34] we successfully described the inte-
rior of a relativistic star along with the existence of a confor-
mal Killing vector field within this f (T ) gravity providing
a set of exact solutions. In connection to f (R) gravity we
observe that there are also several applications with various
aspects on the theory available in the literature [35–37]. A
special and notable application includes the late-time accel-
eration of the Universe, which hasbeenexplained using f (R)
gravity by Carroll et al. [35]. For further reviews on f (R)
gravity model one can check Refs. [38–42].
However, the purpose of the present paper is to consider
another extension of general relativity, the f (R, T ) modified
theory of gravity [43] where the gravitational Lagrangian of
the standard Einstein–Hilbert action is defined by an arbitrary
function of the Ricci scalar R and the trace of the energy-
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