Evolving wormhole in the braneworld scenario

In this paper, evolving wormholes in the context of braneworld scenario are investigated. We have studied the possible dynamic solutions with different forms of Ricci scalar. The possibility of the existence of dynamic traversable wormholes, without resorting to an exotic matter, has been studied. By using the fact that the Einstein field equations are modified in $3+1$ dimensions due to the brane corrections, we investigate the exact solutions which satisfy the null energy condition. Asymptotic flatness is an important property of these solutions. We discuss some physical and mathematical properties of the solutions.

Figure 1

The plot depicts the function $\psi (x)$ against $x$. It shows that $\psi (x)<0$ thorough the entire range of $1<x$ which means the $b(r)<r$ is satisfied everywhere. See the text for details.

Figure 2

The plot depicts the function $H(y,0)$ against $y$. It is clear that $H(y,0)$ is positive thorough the entire ranges of $-2<y<-1$ and $0<y$ which means the NEC is not violated in these ranges. See the text for details.

Figure 3

The plot depicts the general behavior of $y_{+}(t)$ against $t$. It is clear that $y_{+}(t)$ has a maximum at $t=0$ and tends to zero as $t\to \infty$. See the text for details.

Figure 4

The plot depicts the general behavior of $y_{-}(t)$ against $t$. It should be noted that $y_{-}(t)$ has a minimum at $t=0$ and tends to $-2$ as $t\to \infty$. See the text for details.

Figure 5

The plot depicts the general behavior of $H(y,0)$ (solid line),$H(y,2\lambda )$ (dotted line), and $H(y,4\lambda )$ (dashed line), against $y$. It is clear that the general behavior of the $H(y,R)$ is the same for different values of $R$. The only difference is that the range of $y$ for the violation of NEC has been changed. See the text for details.

Figure 6

The plot depicts the general behavior of $\frac{{\rho }_{+}}{\lambda }$ (dashed line), $\frac{p_{+}}{\lambda }$ (dotted line), and ${\omega }_{\mathrm{eff}}$ (solid line), against $\alpha$. It is clear that ${\rho }_{+}$ is positive through the range $\alpha \ge 0$ and changes the sign in $\alpha =0$. It shows that the range $\alpha \ge 0$ is more physically. See the text for details.

Figure 7

The plot depicts the general behavior of $\frac{{\rho }_{-}}{\lambda }$ (dashed line), $\frac{p_{-}}{\lambda }$ (dotted line), and ${\omega }_{\mathrm{eff}}$ (solid line), against $\alpha$. It is clear that ${\rho }_{-}$ is negative through the entire range $-2\le \alpha$ but $p_{-}$ is positive. It shows that this class of solutions is not of great interest. See the text for details.