Stable wormholes on a noncommutative-geometry background admitting a one-parameter group of conformal motions

Abstract

When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al., using a slightly different approach. Accordingly, the main purpose of this paper is to show that the wormhole obtained can be made stable to linearized radial perturbations.

Minimally Deformed Wormholes Inspired by Noncommutative Geometry

“…Concretely, we are going to assume that $$\theta ^{t}_{\ t}(r)$$ is representing the so–called noncommutative Gaussian energy density $$\rho _{G}$$ of a static and spherically symmetric smeared and particle–like gravitational source [ 110–112 ] $$$$\begin{equation} \rho _{G}=\frac{\mu _{G}}{{\left(4\pi \mathbb {M}_{G}\right)}^{3/2}}\text{Exp}{\left(-\frac{r^{2}}{4\mathbb {M}_{G}}\right)}, \end{equation}$$$$and the noncommutative Lorentzian energy density $$\rho _{L}$$ [ 113 ] $$$$\begin{equation} \rho _{L}=\frac{\sqrt {\mathbb {M}_{L}}\mu _{L}}{\pi ^{2}{\left(\mathbb {M}_{L}+r^{2}\right)}^{2}}, \end{equation}$$$$in order to generate two minimally deformed MT wormhole space–times. As mentioned before, these matter profiles have been widely used in the construction of wormhole structures in different gravitational frameworks such as GR, [ 17–19,116 ] Gauss–Bonnet, [ 117 ] $$f(R)$$ [ 118–120 ] and Rastall [ 121 ] theories, to name a few. As matter of fact, profiles () and () are positive defined everywhere and monotonically decreasing functions with increasing r .…”

“…in order to generate two minimally deformed MT wormhole space-times. As mentioned before, these matter profiles have been widely used in the construction of wormhole structures in different gravitational frameworks such as GR, [17][18][19]116] Gauss-Bonnet, [117] f (R) [118][119][120] and Rastall [121] theories, to name a few. As matter of fact, profiles (30) and ( 31) are positive defined everywhere and monotonically decreasing functions with increasing r. Of course, the positivity upon depends on the signature of the parameters 𝜇 G and 𝜇 L .…”

“…[11] Also, using non conventional matter distributions such as a phantom field [12,13] and Chaplygin gas [14] wormhole solutions and their stability were studied. Moreover, incorporation of the so-called conformal motion symmetry, some interesting wormhole solutions have been found in [15][16][17][18][19].…”

Two diverse models of embedding class one

“…To study the effect of conformal symmetry, it is convenient to use line element (1) with the opposite signature [18,19]:…”

The Effect of Conformal Symmetry on Charged Wormholes

“…To study the effect of conformal symmetry, it is convenient to use an alternate form of the metric [14,15]:…”