Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions
Eur. Phys. J. C
Non-minimal coupling of torsion-matter satisfying null energy condition for wormhole solutions
Abdul Jawad 0
Shamaila Rani 0
0 Department of Mathematics, COMSATS Institute of Information Technology , Lahore 54000 , Pakistan
We explore wormhole solutions in a non-minimal torsion-matter coupled gravity by taking an explicit nonminimal coupling between the matter Lagrangian density and an arbitrary function of the torsion scalar. This coupling describes the transfer of energy and momentum between matter and torsion scalar terms. The violation of the null energy condition occurred through an effective energy-momentum tensor incorporating the torsion-matter non-minimal coupling, while normal matter is responsible for supporting the respective wormhole geometries. We consider the energy density in the form of non-monotonically decreasing function along with two types of models. The first model is analogous to the curvature-matter coupling scenario, that is, the torsion scalar with T -matter coupling, while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying the null energy condition. Also, we find that the increasing value of the coupling constant minimizes or vanishes on the violation of the null energy condition through matter.
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1 Introduction
The topological handles which connect distant regions of the
universe as a bridge or tunnel is named a wormhole. The
most amazing thing is the two-way travel through a
wormhole tunnel which happened when the throat remains open –
that is, to prevent the wormhole from collapse at a non-zero
minimum value of the radial coordinate. In order to keep the
throat open, the exotic matter is used which violates the null
energy condition and one elaborates the wormhole
trajectories as hypothetical paths. The violation of the null energy
condition is the basic ingredient to integrate wormhole
solutions. This configuration was first studied by Flamm [
1
] and
then led Einstein and Rosen [
2
] to contribute the successive
steps for the construction of wormhole solutions. The work
of Morris and Thorne [
3
] evoked the wormhole scenario and
led to new directions. The usual types of matter are
considered to satisfy the energy conditions, therefore, some exotic
type matter is employed for these solutions. There exist some
wormhole solutions in semi-classical gravity through
quantum effects such as Hawking evaporation and Casimir effects
[
3,4
] where the energy conditions are violated. One may take
some such types of matter which acted as exotic matter, for
instance, phantom energy [
5–7
], tachyon matter [8],
generalized Chaplygin gas [
9
], some non-minimal kinetic coupling,
etc.
In order to find some realistic sources that support the
wormhole geometry or minimize the usage of exotic
matter, different varieties of wormhole solutions are explored.
These include thin-shell, dynamical, and rotating wormholes
[
10–16
]. However, our concentration goes toward modified
theories of gravity where the effective scenario gives the
violation of the null energy condition and the matter source
supports the wormholes. In f (R) gravity, Lobo and Oliveira [
17
]
found that the higher curvature terms in the effective
energymomentum tensor are responsible for the necessary violation
for the wormhole solutions. They assumed a particular the
shape function along with various fluids to check the
validity of energy conditions. Jamil et al. [
18
] discussed several
static wormhole solutions in this version of gravity with a
noncommutative geometry background through a Gaussian
distribution. They were first to consider a power-law
solution and construct the wormhole geometry as well as analyze
the validity of the energy conditions. Second, they explored
these solutions with the help of the shape function. Taking
into account a Lorentzian distribution of the energy density,
Rahaman et al. [
19
] derived some new exact solutions in the
same manner and gave some viable wormhole solutions.
In extended teleparallel gravity, being a modification of
teleparallel gravity [
20–46
], static as well as dynamical
wormhole solutions are also explored. In this way, Böhmer
et al. [
47
] investigated wormhole solutions in this gravity
by taking some specific f (T ) forms, the shape function as
well as redshift functions which are the basic characteristics
of these solutions. Assuming different fluids such as
barotropic, isotropic, and anisotropic, Jamil et al. [
48
] explored
the possibility of some realistic sources for wormhole
solutions. Sharif and Rani explored the wormhole solutions in
this gravity taking a noncommutative background with a
Gaussian distribution [
49
], dynamical wormhole solutions
[
50
], for the traceless fluid [
51
], with the inclusion of charge
[
52
] and galactic halo scenario [
53
]. They considered some
power-law f (T ) functions for which the effective
energymomentum tensor depending (...truncated)