Sources of matter for wormholes in a k-essence theory

Abstract

In this work, we analyze some matter sources associated with wormhole models within a k-essence theory coupled to the gravitational sector through a phantom scalar field. We adopt a spherically symmetric background in (3+1) dimensions and consider two types of systems: electrically and magnetically charged. In the first case, we consider the generalized Ellis-Bronnikov model, in which we fix the k-essence field exponent to $n=1/2$ and take the parameter $m\ge 2$, where $m$ is the parameter that modifies the area of this wormhole model. From this we obtained the expression for the scalar field, the potential, and the associated electromagnetic functions for any values of the parameter $m\geq{2}$. In the second and third models, we consider the scenario of two wormholes that are structured according to the adjustment of the parameters that define their area function $Σ^2$, and in both cases we adopt $n=1/2$. Finally, we show that the violation of the null energy conditions is conditioned by the parameters of the area function.

Figures (8)

• Figure 1: In the figures above the following values were set $n=1/2$ and $a=F_0=1$. In a) we have the scalar field, b) the potential and in c) the Lagrangian.
• Figure 2: In the figures above the following values were set $q_e=a=1$ and $m=4$. In a) we have the scalar $f(x)$, in b) the electromagnetic scalar as a function of the scalar $P$, and in c) the Lagrangian.
• Figure 3: In the figures above the following values were set $n=1/2$ and $a=F_0=1$. In panels a), b), c) we have the variation of the parameters of the scalar field as a function of the radial coordinate. In panels d), e), f) we have the variation of the potential parameters as a function of the radial coordinate, the in panels g), h), i) we have the variation of the parameters of the Lagrangian function as a function of the radial coordinate.
• Figure 4: In the figures above the following values were set $q_m=d=1$, $c_3=3$, and $b=4$. In a) we have the scalar $f(x)$, in b) the Lagrangian in terms of the radial coordinate $x$, and in c) the Lagrangian $L(f)$.
• Figure 5: In the figures above the following values were set $q_e=d=1$, $c_3=3$, and $b=4$. In a) we have the scalar $f(x)$, in b) the Lagrangian in terms of the radial coordinate $x$, and in c) the Lagrangian $L(f)$. All figures are considering the electric charged case.