Slowly rotating scalar field wormholes: The second order approximation

We discuss rotating wormholes in general relativity with a scalar field with negative kinetic energy. To solve the problem, we use the assumption about slow rotation. The role of a small dimensionless parameter plays the ratio of the linear velocity of rotation of the wormhole’s throat and the velocity of light. We construct the rotating wormhole solution in the second-order approximation with respect to the small parameter. The analysis shows that the asymptotical mass of the rotating wormhole is greater than that of the nonrotating one, and the null energy condition violation in the rotating wormhole spacetime is weaker than that in the nonrotating one.

Figure 1

The graphs of ${\alpha }_0(r)$, ${\beta }_0(r)$, and ${\varphi }_0(r)$ for $a=1$. The thick, middle, and thin curves correspond to $m=0$, 0.5, 1, respectively.

Figure 2

The graphs of ${\alpha }_2(r)$, ${\beta }_2(r)$, ${\rho }_2(r)$, and ${\varphi }_2(r)$ for $a=1$. The thick, middle, and thin curves correspond to $m=0$, 0.5, 1, respectively.

Figure 3

The graph of $\Delta m(\mu )$ for $a=1$.

Figure 4

The graphs of $\Xi (r)$ (thick line) and ${\Xi }_0(r)$ (thin line) for $a=1$.